{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Introduction to atomman: NeighborList class\n",
    "\n",
    "__Lucas M. Hale__, [lucas.hale@nist.gov](mailto:lucas.hale@nist.gov?Subject=ipr-demo), _Materials Science and Engineering Division, NIST_.\n",
    "    \n",
    "[Disclaimers](http://www.nist.gov/public_affairs/disclaimer.cfm) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Introduction<a id='section1'></a>\n",
    "\n",
    "The NeighborList class allows all neighbor atoms within a specified cutoff distance to be identified, and provides a nice interface for accessing each atom's coordination number and list of neighbor atoms. \n",
    "\n",
    "### 1.1. Theory and methodology\n",
    "\n",
    "The NeighborList class uses the nlist() function in atomman/core/nlist.py to built the list of neighbor atoms.  First, the routine defines an orthogonal super-box that fully encompasses the system.  The super-box is then divided into cubic bins of dimensions of cutoff.  Each bin is given a list of atom ids corresponding to both the real atoms in the system as well as ghost atoms from periodic replicas of the system that fall inside the bin's boundaries.\n",
    "\n",
    "For all bins containing at least one real atom, the shortest vector distance between the atoms within that bin and nearby bins are calculated using dvect().  The ids of atoms separated by less than the cutoff distance are added to each other's neighbors list, as long as the ids are not the same or already in the list.\n",
    "\n",
    "**NOTE:** This routine does not differentiate between the different periodic replicas of the atoms.  As such, the system's dimensions should be larger than the cutoff distance used to ensure that atoms are not neighbors of themselves, or periodic replicas of the same atom.\n",
    "\n",
    "*Updated version 1.2.6:* cmult and code options removed as underlying cython code is better integrated and now considerably faster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Library Imports**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "atomman version = 1.4.0\n",
      "Notebook executed on 2021-08-05\n"
     ]
    }
   ],
   "source": [
    "# Standard Python libraries\n",
    "import os\n",
    "import datetime\n",
    "\n",
    "# http://www.numpy.org/\n",
    "import numpy as np\n",
    "\n",
    "# https://github.com/usnistgov/atomman\n",
    "import atomman as am\n",
    "\n",
    "# Show atomman version\n",
    "print('atomman version =', am.__version__)\n",
    "\n",
    "# Show date of Notebook execution\n",
    "print('Notebook executed on', datetime.date.today())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construct a 10x10x10 bcc supercell system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2000\n"
     ]
    }
   ],
   "source": [
    "box = am.Box(a=2.8665, b=2.8665, c=2.8665)\n",
    "atoms = am.Atoms(atype=1, pos=[[0.0, 0.0, 0.0], [0.5, 0.5, 0.5]])\n",
    "system = am.System(atoms=atoms, box=box, scale=True)\n",
    "system = system.supersize(10, 10, 10)\n",
    "print(system.natoms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Identifying neighbors<a id='section2'></a>\n",
    "\n",
    "The list of neighbors is computed during class initialization or by calling the build() method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1. Initialization\n",
    "\n",
    "The NeighborList can be initialized either by identifying neighbors using a system and a cutoff, or by reading in data from model.\n",
    "\n",
    "Parameters\n",
    "\n",
    "- **system** (*atomman.System, optional*) The system to calculate the neighbor list for. Must be given if model is not given.\n",
    "- **cutoff** (*float, optional*) Radial cutoff distance for identifying neighbors.  Must be given if model is not given.\n",
    "- **model** (*str or file-like object, optional*) Gives the file path or content to load.  No other parameters are allowed.    \n",
    "- **initialsize** (*int, optional*) The number of neighbor positions to initially assign to each atom.  Default value is 20.\n",
    "- **deltasize** (*int, optional*) Specifies the number of extra neighbor positions to allow each atom when the number of neighbors exceeds the underlying array size.  Default value is 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "avect =  [28.665,  0.000,  0.000]\n",
      "bvect =  [ 0.000, 28.665,  0.000]\n",
      "cvect =  [ 0.000,  0.000, 28.665]\n",
      "origin = [ 0.000,  0.000,  0.000]\n"
     ]
    }
   ],
   "source": [
    "print(system.box)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate a new NeighborList object\n",
    "neighbors = am.NeighborList(system=system, cutoff=2.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2. The coord attribute\n",
    "\n",
    "The number of neighbors, i.e. coordination, for each atom can be retrieved using the coord attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The coordination of atom 4 = 8\n",
      "Average number of neighbors = 8.0\n"
     ]
    }
   ],
   "source": [
    "print('The coordination of atom 4 =', neighbors.coord[4])\n",
    "print('Average number of neighbors =', neighbors.coord.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3. Per-atom neighbor lists\n",
    "\n",
    "The list of identified neighbors can be obtained using numerical indexing on the NeighborList object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The neighbor atoms of atom 3 are [  2   4  22  24 202 204 222 224]\n"
     ]
    }
   ],
   "source": [
    "print('The neighbor atoms of atom 3 are', neighbors[3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since this is a list of atom indices, it can be easily used to select properties of only the neighbor atoms of one atom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4.29975  1.43325  1.43325]\n",
      " [ 7.16625  1.43325  1.43325]\n",
      " [ 4.29975 27.23175  1.43325]\n",
      " [ 7.16625 27.23175  1.43325]\n",
      " [ 4.29975  1.43325 27.23175]\n",
      " [ 7.16625  1.43325 27.23175]\n",
      " [ 4.29975 27.23175 27.23175]\n",
      " [ 7.16625 27.23175 27.23175]]\n"
     ]
    }
   ],
   "source": [
    "# Show the positions of the neighbor atoms to atom 4\n",
    "print(system.atoms.pos[neighbors[4]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The neighbor lists can also be iterated over for each atom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[   1   19  181  199 1801 1819 1981 1999]\n",
      "[  0   2  20  22 200 202 220 222]\n",
      "[   1    3  181  183 1801 1803 1981 1983]\n",
      "[  2   4  22  24 202 204 222 224]\n",
      "[   3    5  183  185 1803 1805 1983 1985]\n",
      "[  4   6  24  26 204 206 224 226]\n",
      "[   5    7  185  187 1805 1807 1985 1987]\n",
      "[  6   8  26  28 206 208 226 228]\n",
      "[   7    9  187  189 1807 1809 1987 1989]\n",
      "[  8  10  28  30 208 210 228 230]\n",
      "[   9   11  189  191 1809 1811 1989 1991]\n",
      "[ 10  12  30  32 210 212 230 232]\n",
      "[  11   13  191  193 1811 1813 1991 1993]\n",
      "[ 12  14  32  34 212 214 232 234]\n",
      "[  13   15  193  195 1813 1815 1993 1995]\n",
      "[ 14  16  34  36 214 216 234 236]\n",
      "[  15   17  195  197 1815 1817 1995 1997]\n",
      "[ 16  18  36  38 216 218 236 238]\n",
      "[  17   19  197  199 1817 1819 1997 1999]\n",
      "[  0  18  20  38 200 218 220 238]\n",
      "...\n"
     ]
    }
   ],
   "source": [
    "# List the neighbor ids for the first 20 neighbors\n",
    "for i, nlist in enumerate(neighbors):\n",
    "    print(nlist)\n",
    "    \n",
    "    if i == 19:\n",
    "        print('...')\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.48246182 2.48246182 2.48246182 2.48246182 2.48246182 2.48246182\n",
      " 2.48246182 2.48246182]\n",
      "[2.48246182 2.48246182 2.48246182 2.48246182 2.48246182 2.48246182\n",
      " 2.48246182 2.48246182]\n",
      "[2.48246182 2.48246182 2.48246182 2.48246182 2.48246182 2.48246182\n",
      " 2.48246182 2.48246182]\n",
      "[2.48246182 2.48246182 2.48246182 2.48246182 2.48246182 2.48246182\n",
      " 2.48246182 2.48246182]\n",
      "[2.48246182 2.48246182 2.48246182 2.48246182 2.48246182 2.48246182\n",
      " 2.48246182 2.48246182]\n",
      "[2.48246182 2.48246182 2.48246182 2.48246182 2.48246182 2.48246182\n",
      " 2.48246182 2.48246182]\n",
      "[2.48246182 2.48246182 2.48246182 2.48246182 2.48246182 2.48246182\n",
      " 2.48246182 2.48246182]\n",
      "[2.48246182 2.48246182 2.48246182 2.48246182 2.48246182 2.48246182\n",
      " 2.48246182 2.48246182]\n",
      "[2.48246182 2.48246182 2.48246182 2.48246182 2.48246182 2.48246182\n",
      " 2.48246182 2.48246182]\n",
      "[2.48246182 2.48246182 2.48246182 2.48246182 2.48246182 2.48246182\n",
      " 2.48246182 2.48246182]\n",
      "...\n"
     ]
    }
   ],
   "source": [
    "# List the neighbor dmag values for the first 10 neighbors\n",
    "for i, nlist in enumerate(neighbors):\n",
    "    print(system.dmag(i, nlist))\n",
    "    \n",
    "    if i == 9:\n",
    "        print('...')\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. build()<a id='section3'></a>\n",
    "\n",
    "The build() method allows an existing NeighborList object to find neighbors for a new system and cutoff.\n",
    "\n",
    "Parameters\n",
    "\n",
    "- **system** (*atomman.System*) The system to calculate the neighbor list for. Must be given if model is not given.\n",
    "- **cutoff** (*float*) Radial cutoff distance for identifying neighbors.  Must be given if model is not given. \n",
    "- **initialsize** (*int, optional*) The number of neighbor positions to initially assign to each atom.  Default value is 20.\n",
    "- **deltasize** (*int, optional*) Specifies the number of extra neighbor positions to allow each atom when the number of neighbors exceeds the underlying array size.  Default value is 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average number of neighbors = 14.0\n"
     ]
    }
   ],
   "source": [
    "# Identify nearest and next-nearest neighbors with a larger cutoff\n",
    "neighbors.build(system=system, cutoff=2.9)\n",
    "print('Average number of neighbors =', neighbors.coord.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. dump() and load()<a id='section4'></a>\n",
    "\n",
    "The list of neighbors can also be saved to a file using dump() and accessed later using load().  This is useful for large systems where regenerating the list of neighbors is time consuming."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1. dump()\n",
    "\n",
    "Saves the neighbor list to a file.\n",
    "        \n",
    "Parameters\n",
    "\n",
    "- **fname** (*str*) The file name to save the content to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Neighbor list:\n",
      "# The first column gives an atom index.\n",
      "# The rest of the columns are the indexes of the identified neighbors.\n",
      "0 1 2 18 19 20 180 181 199 200 1800 1801 1819 1981 1999\n",
      "1 0 2 3 19 20 21 22 181 200 201 202 220 222 1801\n",
      "2 0 1 3 4 22 181 182 183 202 1801 1802 1803 1981 1983\n",
      "3 1 2 4 5 22 23 24 183 202 203 204 222 224 1803\n",
      "4 2 3 5 6 24 183 184 185 204 1803 1804 1805 1983 1985\n",
      "5 3 4 6 7 24 25 26 185 204 205 206 224 226 1805\n",
      "6 4 5 7 8 26 185 186 187 206 1805 1806 1807 1985 1987\n",
      "7 5 6 8 9 26 27 28 187 206 207 208 226 228 1807\n",
      "8 6 7 9 10 28 187 188 189 208 1807 1808 1809 1987 1989\n",
      "9 7 8 10 11 28 29 30 189 208 209 210 228 230 1809\n",
      "10 8 9 11 12 30 189 190 191 210 1809 1810 1811 1989 1991\n",
      "11 9 10 12 13 30 31 32 191 210 211 212 230 232 1811\n",
      "12 10 11 13 14 32 191 192 193 212 1811 1812 1813 1991 1993\n",
      "13 11 12 14 15 32 33 34 193 212 213 214 232 234 1813\n",
      "14 12 13 15 16 34 193 194 195 214 1813 1814 1815 1993 1995\n",
      "15 13 14 16 17 34 35 36 195 214 215 216 234 236 1815\n",
      "16 14 15 17 18 36 195 196 197 216 1815 1816 1817 1995 1997\n",
      "17 15 16 18 19 36 37 38 197 216 217 218 236 238 1817\n",
      "18 0 16 17 19 38 197 198 199 218 1817 1818 1819 1997 1999\n",
      "19 0 1 17 18 20 38 39 199 200 218 219 220 238 1819\n",
      "20 0 1 19 21 22 38 39 40 220 1801 1819 1820 1821 1839\n",
      "21 1 20 22 23 39 40 41 42 220 221 222 240 242 1821\n",
      "22 1 2 3 20 21 23 24 42 222 1801 1803 1821 1822 1823\n",
      "23 3 21 22 24 25 42 43 44 222 223 224 242 244 1823\n",
      "24 3 4 5 22 23 25 26 44 224 1803 1805 1823 1824 1825\n",
      "25 5 23 24 26 27 44 45 46 224 225 226 244 246 1825\n",
      "26 5 6 7 24 25 27 28 46 226 1805 1807 1825 1826 1827\n",
      "27 7 25 26 28 29 46 47 48 226 227 228 246 248 1827\n",
      "28 7 8 9 26 27 29 30 48 228 1807 1809 1827 1828 1829\n",
      "29 9 27 28 30 31 48 49 50 228 229 230 248 250 1829\n",
      "30 9 10 11 28 29 31 32 50 230 1809 1811 1829 1830 1831\n",
      "31 11 29 30 32 33 50 51 52 230 231 232 250 252 1831\n",
      "32 11 12 13 30 31 33 34 52 232 1811 1813 1831 1832 1833\n",
      "33 13 31 32 34 35 52 53 54 232 233 234 252 254 1833\n",
      "34 13 14 15 32 33 35 36 54 234 1813 1815 1833 1834 1835\n",
      "35 15 33 34 36 37 54 55 56 234 235 236 254 256 1835\n",
      "36 15 16 17 34 35 37 38 56 236 1815 1817 1835 1836 1837\n",
      "37 17 35 36 38 39 56 57 58 236 237 238 256 258 1837\n",
      "38 17 18 19 20 36 37 39 58 238 1817 1819 1837 1838 1839\n",
      "39 19 20 21 37 38 40 58 59 220 238 239 240 258 1839\n",
      "40 20 21 39 41 42 58 59 60 240 1821 1839 1840 1841 1859\n",
      "41 21 40 42 43 59 60 61 62 240 241 242 260 262 1841\n",
      "42 21 22 23 40 41 43 44 62 242 1821 1823 1841 1842 1843\n",
      "43 23 41 42 44 45 62 63 64 242 243 244 262 264 1843\n",
      "44 23 24 25 42 43 45 46 64 244 1823 1825 1843 1844 1845\n",
      "45 25 43 44 46 47 64 65 66 244 245 246 264 266 1845\n",
      "46 25 26 27 44 45 47 48 66 246 1825 1827 1845 1846 1847\n",
      "47 27 45 46 48 49 66 67 68 246 247 248 266 268 1847\n",
      "48 27 28 29 46 47 49 50 68 248 1827 1829 1847 1848 1849\n",
      "49 29 47 48 50 51 68 69 70 248 249 250 268 270 1849\n",
      "50 29 30 31 48 49 51 52 70 250 1829 1831 1849 1850 1851\n",
      "51 31 49 50 52 53 70 71 72 250 251 252 270 272 1851\n",
      "52 31 32 33 50 51 53 54 72 252 1831 1833 1851 1852 1853\n",
      "53 33 51 52 54 55 72 73 74 252 253 254 272 274 1853\n",
      "54 33 34 35 52 53 55 56 74 254 1833 1835 1853 1854 1855\n",
      "55 35 53 54 56 57 74 75 76 254 255 256 274 276 1855\n",
      "56 35 36 37 54 55 57 58 76 256 1835 1837 1855 1856 1857\n",
      "57 37 55 56 58 59 76 77 78 256 257 258 276 278 1857\n",
      "58 37 38 39 40 56 57 59 78 258 1837 1839 1857 1858 1859\n",
      "59 39 40 41 57 58 60 78 79 240 258 259 260 278 1859\n",
      "60 40 41 59 61 62 78 79 80 260 1841 1859 1860 1861 1879\n",
      "61 41 60 62 63 79 80 81 82 260 261 262 280 282 1861\n",
      "62 41 42 43 60 61 63 64 82 262 1841 1843 1861 1862 1863\n",
      "63 43 61 62 64 65 82 83 84 262 263 264 282 284 1863\n",
      "64 43 44 45 62 63 65 66 84 264 1843 1845 1863 1864 1865\n",
      "65 45 63 64 66 67 84 85 86 264 265 266 284 286 1865\n",
      "66 45 46 47 64 65 67 68 86 266 1845 1847 1865 1866 1867\n",
      "67 47 65 66 68 69 86 87 88 266 267 268 286 288 1867\n",
      "68 47 48 49 66 67 69 70 88 268 1847 1849 1867 1868 1869\n",
      "69 49 67 68 70 71 88 89 90 268 269 270 288 290 1869\n",
      "70 49 50 51 68 69 71 72 90 270 1849 1851 1869 1870 1871\n",
      "71 51 69 70 72 73 90 91 92 270 271 272 290 292 1871\n",
      "72 51 52 53 70 71 73 74 92 272 1851 1853 1871 1872 1873\n",
      "73 53 71 72 74 75 92 93 94 272 273 274 292 294 1873\n",
      "74 53 54 55 72 73 75 76 94 274 1853 1855 1873 1874 1875\n",
      "75 55 73 74 76 77 94 95 96 274 275 276 294 296 1875\n",
      "76 55 56 57 74 75 77 78 96 276 1855 1857 1875 1876 1877\n",
      "77 57 75 76 78 79 96 97 98 276 277 278 296 298 1877\n",
      "78 57 58 59 60 76 77 79 98 278 1857 1859 1877 1878 1879\n",
      "79 59 60 61 77 78 80 98 99 260 278 279 280 298 1879\n",
      "80 60 61 79 81 82 98 99 100 280 1861 1879 1880 1881 1899\n",
      "81 61 80 82 83 99 100 101 102 280 281 282 300 302 1881\n",
      "82 61 62 63 80 81 83 84 102 282 1861 1863 1881 1882 1883\n",
      "83 63 81 82 84 85 102 103 104 282 283 284 302 304 1883\n",
      "84 63 64 65 82 83 85 86 104 284 1863 1865 1883 1884 1885\n",
      "85 65 83 84 86 87 104 105 106 284 285 286 304 306 1885\n",
      "86 65 66 67 84 85 87 88 106 286 1865 1867 1885 1886 1887\n",
      "87 67 85 86 88 89 106 107 108 286 287 288 306 308 1887\n",
      "88 67 68 69 86 87 89 90 108 288 1867 1869 1887 1888 1889\n",
      "89 69 87 88 90 91 108 109 110 288 289 290 308 310 1889\n",
      "90 69 70 71 88 89 91 92 110 290 1869 1871 1889 1890 1891\n",
      "91 71 89 90 92 93 110 111 112 290 291 292 310 312 1891\n",
      "92 71 72 73 90 91 93 94 112 292 1871 1873 1891 1892 1893\n",
      "93 73 91 92 94 95 112 113 114 292 293 294 312 314 1893\n",
      "94 73 74 75 92 93 95 96 114 294 1873 1875 1893 1894 1895\n",
      "95 75 93 94 96 97 114 115 116 294 295 296 314 316 1895\n",
      "96 75 76 77 94 95 97 98 116 296 1875 1877 1895 1896 1897\n",
      "97 77 95 96 98 99 116 117 118 296 297 298 316 318 1897\n",
      "98 77 78 79 80 96 97 99 118 298 1877 1879 1897 1898 1899\n",
      "99 79 80 81 97 98 100 118 119 280 298 299 300 318 1899\n",
      "100 80 81 99 101 102 118 119 120 300 1881 1899 1900 1901 1919\n",
      "101 81 100 102 103 119 120 121 122 300 301 302 320 322 1901\n",
      "102 81 82 83 100 101 103 104 122 302 1881 1883 1901 1902 1903\n",
      "103 83 101 102 104 105 122 123 124 302 303 304 322 324 1903\n",
      "104 83 84 85 102 103 105 106 124 304 1883 1885 1903 1904 1905\n",
      "105 85 103 104 106 107 124 125 126 304 305 306 324 326 1905\n",
      "106 85 86 87 104 105 107 108 126 306 1885 1887 1905 1906 1907\n",
      "107 87 105 106 108 109 126 127 128 306 307 308 326 328 1907\n",
      "108 87 88 89 106 107 109 110 128 308 1887 1889 1907 1908 1909\n",
      "109 89 107 108 110 111 128 129 130 308 309 310 328 330 1909\n",
      "110 89 90 91 108 109 111 112 130 310 1889 1891 1909 1910 1911\n",
      "111 91 109 110 112 113 130 131 132 310 311 312 330 332 1911\n",
      "112 91 92 93 110 111 113 114 132 312 1891 1893 1911 1912 1913\n",
      "113 93 111 112 114 115 132 133 134 312 313 314 332 334 1913\n",
      "114 93 94 95 112 113 115 116 134 314 1893 1895 1913 1914 1915\n",
      "115 95 113 114 116 117 134 135 136 314 315 316 334 336 1915\n",
      "116 95 96 97 114 115 117 118 136 316 1895 1897 1915 1916 1917\n",
      "117 97 115 116 118 119 136 137 138 316 317 318 336 338 1917\n",
      "118 97 98 99 100 116 117 119 138 318 1897 1899 1917 1918 1919\n",
      "119 99 100 101 117 118 120 138 139 300 318 319 320 338 1919\n",
      "120 100 101 119 121 122 138 139 140 320 1901 1919 1920 1921 1939\n",
      "121 101 120 122 123 139 140 141 142 320 321 322 340 342 1921\n",
      "122 101 102 103 120 121 123 124 142 322 1901 1903 1921 1922 1923\n",
      "123 103 121 122 124 125 142 143 144 322 323 324 342 344 1923\n",
      "124 103 104 105 122 123 125 126 144 324 1903 1905 1923 1924 1925\n",
      "125 105 123 124 126 127 144 145 146 324 325 326 344 346 1925\n",
      "126 105 106 107 124 125 127 128 146 326 1905 1907 1925 1926 1927\n",
      "127 107 125 126 128 129 146 147 148 326 327 328 346 348 1927\n",
      "128 107 108 109 126 127 129 130 148 328 1907 1909 1927 1928 1929\n",
      "129 109 127 128 130 131 148 149 150 328 329 330 348 350 1929\n",
      "130 109 110 111 128 129 131 132 150 330 1909 1911 1929 1930 1931\n",
      "131 111 129 130 132 133 150 151 152 330 331 332 350 352 1931\n",
      "132 111 112 113 130 131 133 134 152 332 1911 1913 1931 1932 1933\n",
      "133 113 131 132 134 135 152 153 154 332 333 334 352 354 1933\n",
      "134 113 114 115 132 133 135 136 154 334 1913 1915 1933 1934 1935\n",
      "135 115 133 134 136 137 154 155 156 334 335 336 354 356 1935\n",
      "136 115 116 117 134 135 137 138 156 336 1915 1917 1935 1936 1937\n",
      "137 117 135 136 138 139 156 157 158 336 337 338 356 358 1937\n",
      "138 117 118 119 120 136 137 139 158 338 1917 1919 1937 1938 1939\n",
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      "774 553 555 573 574 575 753 754 755 772 773 775 776 794 974\n",
      "775 575 755 773 774 776 777 794 795 796 974 975 976 994 996\n",
      "776 555 557 575 576 577 755 756 757 774 775 777 778 796 976\n",
      "777 577 757 775 776 778 779 796 797 798 976 977 978 996 998\n",
      "778 557 559 577 578 579 757 758 759 760 776 777 779 798 978\n",
      "779 579 759 760 761 777 778 780 798 799 960 978 979 980 998\n",
      "780 561 579 580 581 599 600 760 761 779 781 782 798 799 980\n",
      "781 581 600 601 602 761 780 782 783 799 800 802 980 981 982\n",
      "782 561 563 581 582 583 602 761 762 763 780 781 783 784 982\n",
      "783 583 602 603 604 763 781 782 784 785 802 804 982 983 984\n",
      "784 563 565 583 584 585 604 763 764 765 782 783 785 786 984\n",
      "785 585 604 605 606 765 783 784 786 787 804 806 984 985 986\n",
      "786 565 567 585 586 587 606 765 766 767 784 785 787 788 986\n",
      "787 587 606 607 608 767 785 786 788 789 806 808 986 987 988\n",
      "788 567 569 587 588 589 608 767 768 769 786 787 789 790 988\n",
      "789 589 608 609 610 769 787 788 790 791 808 810 988 989 990\n",
      "790 569 571 589 590 591 610 769 770 771 788 789 791 792 990\n",
      "791 591 610 611 612 771 789 790 792 793 810 812 990 991 992\n",
      "792 571 573 591 592 593 612 771 772 773 790 791 793 794 992\n",
      "793 593 612 613 614 773 791 792 794 795 812 814 992 993 994\n",
      "794 573 575 593 594 595 614 773 774 775 792 793 795 796 994\n",
      "795 595 614 615 616 775 793 794 796 797 814 816 994 995 996\n",
      "796 575 577 595 596 597 616 775 776 777 794 795 797 798 996\n",
      "797 597 616 617 618 777 795 796 798 799 816 818 996 997 998\n",
      "798 577 579 597 598 599 618 777 778 779 780 796 797 799 998\n",
      "799 599 600 618 619 779 780 781 797 798 800 818 980 998 999\n",
      "800 600 601 619 781 799 801 802 818 819 820 980 981 999 1000\n",
      "801 601 800 802 803 819 820 821 822 981 1000 1001 1002 1020 1022\n",
      "802 601 602 603 781 783 800 801 803 804 822 981 982 983 1002\n",
      "803 603 801 802 804 805 822 823 824 983 1002 1003 1004 1022 1024\n",
      "804 603 604 605 783 785 802 803 805 806 824 983 984 985 1004\n",
      "805 605 803 804 806 807 824 825 826 985 1004 1005 1006 1024 1026\n",
      "806 605 606 607 785 787 804 805 807 808 826 985 986 987 1006\n",
      "807 607 805 806 808 809 826 827 828 987 1006 1007 1008 1026 1028\n",
      "808 607 608 609 787 789 806 807 809 810 828 987 988 989 1008\n",
      "809 609 807 808 810 811 828 829 830 989 1008 1009 1010 1028 1030\n",
      "810 609 610 611 789 791 808 809 811 812 830 989 990 991 1010\n",
      "811 611 809 810 812 813 830 831 832 991 1010 1011 1012 1030 1032\n",
      "812 611 612 613 791 793 810 811 813 814 832 991 992 993 1012\n",
      "813 613 811 812 814 815 832 833 834 993 1012 1013 1014 1032 1034\n",
      "814 613 614 615 793 795 812 813 815 816 834 993 994 995 1014\n",
      "815 615 813 814 816 817 834 835 836 995 1014 1015 1016 1034 1036\n",
      "816 615 616 617 795 797 814 815 817 818 836 995 996 997 1016\n",
      "817 617 815 816 818 819 836 837 838 997 1016 1017 1018 1036 1038\n",
      "818 617 618 619 797 799 800 816 817 819 838 997 998 999 1018\n",
      "819 619 800 801 817 818 820 838 839 999 1000 1018 1019 1020 1038\n",
      "820 601 619 620 621 639 800 801 819 821 822 838 839 840 1020\n",
      "821 621 801 820 822 823 839 840 841 842 1020 1021 1022 1040 1042\n",
      "822 601 603 621 622 623 801 802 803 820 821 823 824 842 1022\n",
      "823 623 803 821 822 824 825 842 843 844 1022 1023 1024 1042 1044\n",
      "824 603 605 623 624 625 803 804 805 822 823 825 826 844 1024\n",
      "825 625 805 823 824 826 827 844 845 846 1024 1025 1026 1044 1046\n",
      "826 605 607 625 626 627 805 806 807 824 825 827 828 846 1026\n",
      "827 627 807 825 826 828 829 846 847 848 1026 1027 1028 1046 1048\n",
      "828 607 609 627 628 629 807 808 809 826 827 829 830 848 1028\n",
      "829 629 809 827 828 830 831 848 849 850 1028 1029 1030 1048 1050\n",
      "830 609 611 629 630 631 809 810 811 828 829 831 832 850 1030\n",
      "831 631 811 829 830 832 833 850 851 852 1030 1031 1032 1050 1052\n",
      "832 611 613 631 632 633 811 812 813 830 831 833 834 852 1032\n",
      "833 633 813 831 832 834 835 852 853 854 1032 1033 1034 1052 1054\n",
      "834 613 615 633 634 635 813 814 815 832 833 835 836 854 1034\n",
      "835 635 815 833 834 836 837 854 855 856 1034 1035 1036 1054 1056\n",
      "836 615 617 635 636 637 815 816 817 834 835 837 838 856 1036\n",
      "837 637 817 835 836 838 839 856 857 858 1036 1037 1038 1056 1058\n",
      "838 617 619 637 638 639 817 818 819 820 836 837 839 858 1038\n",
      "839 639 819 820 821 837 838 840 858 859 1020 1038 1039 1040 1058\n",
      "840 621 639 640 641 659 820 821 839 841 842 858 859 860 1040\n",
      "841 641 821 840 842 843 859 860 861 862 1040 1041 1042 1060 1062\n",
      "842 621 623 641 642 643 821 822 823 840 841 843 844 862 1042\n",
      "843 643 823 841 842 844 845 862 863 864 1042 1043 1044 1062 1064\n",
      "844 623 625 643 644 645 823 824 825 842 843 845 846 864 1044\n",
      "845 645 825 843 844 846 847 864 865 866 1044 1045 1046 1064 1066\n",
      "846 625 627 645 646 647 825 826 827 844 845 847 848 866 1046\n",
      "847 647 827 845 846 848 849 866 867 868 1046 1047 1048 1066 1068\n",
      "848 627 629 647 648 649 827 828 829 846 847 849 850 868 1048\n",
      "849 649 829 847 848 850 851 868 869 870 1048 1049 1050 1068 1070\n",
      "850 629 631 649 650 651 829 830 831 848 849 851 852 870 1050\n",
      "851 651 831 849 850 852 853 870 871 872 1050 1051 1052 1070 1072\n",
      "852 631 633 651 652 653 831 832 833 850 851 853 854 872 1052\n",
      "853 653 833 851 852 854 855 872 873 874 1052 1053 1054 1072 1074\n",
      "854 633 635 653 654 655 833 834 835 852 853 855 856 874 1054\n",
      "855 655 835 853 854 856 857 874 875 876 1054 1055 1056 1074 1076\n",
      "856 635 637 655 656 657 835 836 837 854 855 857 858 876 1056\n",
      "857 657 837 855 856 858 859 876 877 878 1056 1057 1058 1076 1078\n",
      "858 637 639 657 658 659 837 838 839 840 856 857 859 878 1058\n",
      "859 659 839 840 841 857 858 860 878 879 1040 1058 1059 1060 1078\n",
      "860 641 659 660 661 679 840 841 859 861 862 878 879 880 1060\n",
      "861 661 841 860 862 863 879 880 881 882 1060 1061 1062 1080 1082\n",
      "862 641 643 661 662 663 841 842 843 860 861 863 864 882 1062\n",
      "863 663 843 861 862 864 865 882 883 884 1062 1063 1064 1082 1084\n",
      "864 643 645 663 664 665 843 844 845 862 863 865 866 884 1064\n",
      "865 665 845 863 864 866 867 884 885 886 1064 1065 1066 1084 1086\n",
      "866 645 647 665 666 667 845 846 847 864 865 867 868 886 1066\n",
      "867 667 847 865 866 868 869 886 887 888 1066 1067 1068 1086 1088\n",
      "868 647 649 667 668 669 847 848 849 866 867 869 870 888 1068\n",
      "869 669 849 867 868 870 871 888 889 890 1068 1069 1070 1088 1090\n",
      "870 649 651 669 670 671 849 850 851 868 869 871 872 890 1070\n",
      "871 671 851 869 870 872 873 890 891 892 1070 1071 1072 1090 1092\n",
      "872 651 653 671 672 673 851 852 853 870 871 873 874 892 1072\n",
      "873 673 853 871 872 874 875 892 893 894 1072 1073 1074 1092 1094\n",
      "874 653 655 673 674 675 853 854 855 872 873 875 876 894 1074\n",
      "875 675 855 873 874 876 877 894 895 896 1074 1075 1076 1094 1096\n",
      "876 655 657 675 676 677 855 856 857 874 875 877 878 896 1076\n",
      "877 677 857 875 876 878 879 896 897 898 1076 1077 1078 1096 1098\n",
      "878 657 659 677 678 679 857 858 859 860 876 877 879 898 1078\n",
      "879 679 859 860 861 877 878 880 898 899 1060 1078 1079 1080 1098\n",
      "880 661 679 680 681 699 860 861 879 881 882 898 899 900 1080\n",
      "881 681 861 880 882 883 899 900 901 902 1080 1081 1082 1100 1102\n",
      "882 661 663 681 682 683 861 862 863 880 881 883 884 902 1082\n",
      "883 683 863 881 882 884 885 902 903 904 1082 1083 1084 1102 1104\n",
      "884 663 665 683 684 685 863 864 865 882 883 885 886 904 1084\n",
      "885 685 865 883 884 886 887 904 905 906 1084 1085 1086 1104 1106\n",
      "886 665 667 685 686 687 865 866 867 884 885 887 888 906 1086\n",
      "887 687 867 885 886 888 889 906 907 908 1086 1087 1088 1106 1108\n",
      "888 667 669 687 688 689 867 868 869 886 887 889 890 908 1088\n",
      "889 689 869 887 888 890 891 908 909 910 1088 1089 1090 1108 1110\n",
      "890 669 671 689 690 691 869 870 871 888 889 891 892 910 1090\n",
      "891 691 871 889 890 892 893 910 911 912 1090 1091 1092 1110 1112\n",
      "892 671 673 691 692 693 871 872 873 890 891 893 894 912 1092\n",
      "893 693 873 891 892 894 895 912 913 914 1092 1093 1094 1112 1114\n",
      "894 673 675 693 694 695 873 874 875 892 893 895 896 914 1094\n",
      "895 695 875 893 894 896 897 914 915 916 1094 1095 1096 1114 1116\n",
      "896 675 677 695 696 697 875 876 877 894 895 897 898 916 1096\n",
      "897 697 877 895 896 898 899 916 917 918 1096 1097 1098 1116 1118\n",
      "898 677 679 697 698 699 877 878 879 880 896 897 899 918 1098\n",
      "899 699 879 880 881 897 898 900 918 919 1080 1098 1099 1100 1118\n",
      "900 681 699 700 701 719 880 881 899 901 902 918 919 920 1100\n",
      "901 701 881 900 902 903 919 920 921 922 1100 1101 1102 1120 1122\n",
      "902 681 683 701 702 703 881 882 883 900 901 903 904 922 1102\n",
      "903 703 883 901 902 904 905 922 923 924 1102 1103 1104 1122 1124\n",
      "904 683 685 703 704 705 883 884 885 902 903 905 906 924 1104\n",
      "905 705 885 903 904 906 907 924 925 926 1104 1105 1106 1124 1126\n",
      "906 685 687 705 706 707 885 886 887 904 905 907 908 926 1106\n",
      "907 707 887 905 906 908 909 926 927 928 1106 1107 1108 1126 1128\n",
      "908 687 689 707 708 709 887 888 889 906 907 909 910 928 1108\n",
      "909 709 889 907 908 910 911 928 929 930 1108 1109 1110 1128 1130\n",
      "910 689 691 709 710 711 889 890 891 908 909 911 912 930 1110\n",
      "911 711 891 909 910 912 913 930 931 932 1110 1111 1112 1130 1132\n",
      "912 691 693 711 712 713 891 892 893 910 911 913 914 932 1112\n",
      "913 713 893 911 912 914 915 932 933 934 1112 1113 1114 1132 1134\n",
      "914 693 695 713 714 715 893 894 895 912 913 915 916 934 1114\n",
      "915 715 895 913 914 916 917 934 935 936 1114 1115 1116 1134 1136\n",
      "916 695 697 715 716 717 895 896 897 914 915 917 918 936 1116\n",
      "917 717 897 915 916 918 919 936 937 938 1116 1117 1118 1136 1138\n",
      "918 697 699 717 718 719 897 898 899 900 916 917 919 938 1118\n",
      "919 719 899 900 901 917 918 920 938 939 1100 1118 1119 1120 1138\n",
      "920 701 719 720 721 739 900 901 919 921 922 938 939 940 1120\n",
      "921 721 901 920 922 923 939 940 941 942 1120 1121 1122 1140 1142\n",
      "922 701 703 721 722 723 901 902 903 920 921 923 924 942 1122\n",
      "923 723 903 921 922 924 925 942 943 944 1122 1123 1124 1142 1144\n",
      "924 703 705 723 724 725 903 904 905 922 923 925 926 944 1124\n",
      "925 725 905 923 924 926 927 944 945 946 1124 1125 1126 1144 1146\n",
      "926 705 707 725 726 727 905 906 907 924 925 927 928 946 1126\n",
      "927 727 907 925 926 928 929 946 947 948 1126 1127 1128 1146 1148\n",
      "928 707 709 727 728 729 907 908 909 926 927 929 930 948 1128\n",
      "929 729 909 927 928 930 931 948 949 950 1128 1129 1130 1148 1150\n",
      "930 709 711 729 730 731 909 910 911 928 929 931 932 950 1130\n",
      "931 731 911 929 930 932 933 950 951 952 1130 1131 1132 1150 1152\n",
      "932 711 713 731 732 733 911 912 913 930 931 933 934 952 1132\n",
      "933 733 913 931 932 934 935 952 953 954 1132 1133 1134 1152 1154\n",
      "934 713 715 733 734 735 913 914 915 932 933 935 936 954 1134\n",
      "935 735 915 933 934 936 937 954 955 956 1134 1135 1136 1154 1156\n",
      "936 715 717 735 736 737 915 916 917 934 935 937 938 956 1136\n",
      "937 737 917 935 936 938 939 956 957 958 1136 1137 1138 1156 1158\n",
      "938 717 719 737 738 739 917 918 919 920 936 937 939 958 1138\n",
      "939 739 919 920 921 937 938 940 958 959 1120 1138 1139 1140 1158\n",
      "940 721 739 740 741 759 920 921 939 941 942 958 959 960 1140\n",
      "941 741 921 940 942 943 959 960 961 962 1140 1141 1142 1160 1162\n",
      "942 721 723 741 742 743 921 922 923 940 941 943 944 962 1142\n",
      "943 743 923 941 942 944 945 962 963 964 1142 1143 1144 1162 1164\n",
      "944 723 725 743 744 745 923 924 925 942 943 945 946 964 1144\n",
      "945 745 925 943 944 946 947 964 965 966 1144 1145 1146 1164 1166\n",
      "946 725 727 745 746 747 925 926 927 944 945 947 948 966 1146\n",
      "947 747 927 945 946 948 949 966 967 968 1146 1147 1148 1166 1168\n",
      "948 727 729 747 748 749 927 928 929 946 947 949 950 968 1148\n",
      "949 749 929 947 948 950 951 968 969 970 1148 1149 1150 1168 1170\n",
      "950 729 731 749 750 751 929 930 931 948 949 951 952 970 1150\n",
      "951 751 931 949 950 952 953 970 971 972 1150 1151 1152 1170 1172\n",
      "952 731 733 751 752 753 931 932 933 950 951 953 954 972 1152\n",
      "953 753 933 951 952 954 955 972 973 974 1152 1153 1154 1172 1174\n",
      "954 733 735 753 754 755 933 934 935 952 953 955 956 974 1154\n",
      "955 755 935 953 954 956 957 974 975 976 1154 1155 1156 1174 1176\n",
      "956 735 737 755 756 757 935 936 937 954 955 957 958 976 1156\n",
      "957 757 937 955 956 958 959 976 977 978 1156 1157 1158 1176 1178\n",
      "958 737 739 757 758 759 937 938 939 940 956 957 959 978 1158\n",
      "959 759 939 940 941 957 958 960 978 979 1140 1158 1159 1160 1178\n",
      "960 741 759 760 761 779 940 941 959 961 962 978 979 980 1160\n",
      "961 761 941 960 962 963 979 980 981 982 1160 1161 1162 1180 1182\n",
      "962 741 743 761 762 763 941 942 943 960 961 963 964 982 1162\n",
      "963 763 943 961 962 964 965 982 983 984 1162 1163 1164 1182 1184\n",
      "964 743 745 763 764 765 943 944 945 962 963 965 966 984 1164\n",
      "965 765 945 963 964 966 967 984 985 986 1164 1165 1166 1184 1186\n",
      "966 745 747 765 766 767 945 946 947 964 965 967 968 986 1166\n",
      "967 767 947 965 966 968 969 986 987 988 1166 1167 1168 1186 1188\n",
      "968 747 749 767 768 769 947 948 949 966 967 969 970 988 1168\n",
      "969 769 949 967 968 970 971 988 989 990 1168 1169 1170 1188 1190\n",
      "970 749 751 769 770 771 949 950 951 968 969 971 972 990 1170\n",
      "971 771 951 969 970 972 973 990 991 992 1170 1171 1172 1190 1192\n",
      "972 751 753 771 772 773 951 952 953 970 971 973 974 992 1172\n",
      "973 773 953 971 972 974 975 992 993 994 1172 1173 1174 1192 1194\n",
      "974 753 755 773 774 775 953 954 955 972 973 975 976 994 1174\n",
      "975 775 955 973 974 976 977 994 995 996 1174 1175 1176 1194 1196\n",
      "976 755 757 775 776 777 955 956 957 974 975 977 978 996 1176\n",
      "977 777 957 975 976 978 979 996 997 998 1176 1177 1178 1196 1198\n",
      "978 757 759 777 778 779 957 958 959 960 976 977 979 998 1178\n",
      "979 779 959 960 961 977 978 980 998 999 1160 1178 1179 1180 1198\n",
      "980 761 779 780 781 799 800 960 961 979 981 982 998 999 1180\n",
      "981 781 800 801 802 961 980 982 983 999 1000 1002 1180 1181 1182\n",
      "982 761 763 781 782 783 802 961 962 963 980 981 983 984 1182\n",
      "983 783 802 803 804 963 981 982 984 985 1002 1004 1182 1183 1184\n",
      "984 763 765 783 784 785 804 963 964 965 982 983 985 986 1184\n",
      "985 785 804 805 806 965 983 984 986 987 1004 1006 1184 1185 1186\n",
      "986 765 767 785 786 787 806 965 966 967 984 985 987 988 1186\n",
      "987 787 806 807 808 967 985 986 988 989 1006 1008 1186 1187 1188\n",
      "988 767 769 787 788 789 808 967 968 969 986 987 989 990 1188\n",
      "989 789 808 809 810 969 987 988 990 991 1008 1010 1188 1189 1190\n",
      "990 769 771 789 790 791 810 969 970 971 988 989 991 992 1190\n",
      "991 791 810 811 812 971 989 990 992 993 1010 1012 1190 1191 1192\n",
      "992 771 773 791 792 793 812 971 972 973 990 991 993 994 1192\n",
      "993 793 812 813 814 973 991 992 994 995 1012 1014 1192 1193 1194\n",
      "994 773 775 793 794 795 814 973 974 975 992 993 995 996 1194\n",
      "995 795 814 815 816 975 993 994 996 997 1014 1016 1194 1195 1196\n",
      "996 775 777 795 796 797 816 975 976 977 994 995 997 998 1196\n",
      "997 797 816 817 818 977 995 996 998 999 1016 1018 1196 1197 1198\n",
      "998 777 779 797 798 799 818 977 978 979 980 996 997 999 1198\n",
      "999 799 800 818 819 979 980 981 997 998 1000 1018 1180 1198 1199\n",
      "1000 800 801 819 981 999 1001 1002 1018 1019 1020 1180 1181 1199 1200\n",
      "1001 801 1000 1002 1003 1019 1020 1021 1022 1181 1200 1201 1202 1220 1222\n",
      "1002 801 802 803 981 983 1000 1001 1003 1004 1022 1181 1182 1183 1202\n",
      "1003 803 1001 1002 1004 1005 1022 1023 1024 1183 1202 1203 1204 1222 1224\n",
      "1004 803 804 805 983 985 1002 1003 1005 1006 1024 1183 1184 1185 1204\n",
      "1005 805 1003 1004 1006 1007 1024 1025 1026 1185 1204 1205 1206 1224 1226\n",
      "1006 805 806 807 985 987 1004 1005 1007 1008 1026 1185 1186 1187 1206\n",
      "1007 807 1005 1006 1008 1009 1026 1027 1028 1187 1206 1207 1208 1226 1228\n",
      "1008 807 808 809 987 989 1006 1007 1009 1010 1028 1187 1188 1189 1208\n",
      "1009 809 1007 1008 1010 1011 1028 1029 1030 1189 1208 1209 1210 1228 1230\n",
      "1010 809 810 811 989 991 1008 1009 1011 1012 1030 1189 1190 1191 1210\n",
      "1011 811 1009 1010 1012 1013 1030 1031 1032 1191 1210 1211 1212 1230 1232\n",
      "1012 811 812 813 991 993 1010 1011 1013 1014 1032 1191 1192 1193 1212\n",
      "1013 813 1011 1012 1014 1015 1032 1033 1034 1193 1212 1213 1214 1232 1234\n",
      "1014 813 814 815 993 995 1012 1013 1015 1016 1034 1193 1194 1195 1214\n",
      "1015 815 1013 1014 1016 1017 1034 1035 1036 1195 1214 1215 1216 1234 1236\n",
      "1016 815 816 817 995 997 1014 1015 1017 1018 1036 1195 1196 1197 1216\n",
      "1017 817 1015 1016 1018 1019 1036 1037 1038 1197 1216 1217 1218 1236 1238\n",
      "1018 817 818 819 997 999 1000 1016 1017 1019 1038 1197 1198 1199 1218\n",
      "1019 819 1000 1001 1017 1018 1020 1038 1039 1199 1200 1218 1219 1220 1238\n",
      "1020 801 819 820 821 839 1000 1001 1019 1021 1022 1038 1039 1040 1220\n",
      "1021 821 1001 1020 1022 1023 1039 1040 1041 1042 1220 1221 1222 1240 1242\n",
      "1022 801 803 821 822 823 1001 1002 1003 1020 1021 1023 1024 1042 1222\n",
      "1023 823 1003 1021 1022 1024 1025 1042 1043 1044 1222 1223 1224 1242 1244\n",
      "1024 803 805 823 824 825 1003 1004 1005 1022 1023 1025 1026 1044 1224\n",
      "1025 825 1005 1023 1024 1026 1027 1044 1045 1046 1224 1225 1226 1244 1246\n",
      "1026 805 807 825 826 827 1005 1006 1007 1024 1025 1027 1028 1046 1226\n",
      "1027 827 1007 1025 1026 1028 1029 1046 1047 1048 1226 1227 1228 1246 1248\n",
      "1028 807 809 827 828 829 1007 1008 1009 1026 1027 1029 1030 1048 1228\n",
      "1029 829 1009 1027 1028 1030 1031 1048 1049 1050 1228 1229 1230 1248 1250\n",
      "1030 809 811 829 830 831 1009 1010 1011 1028 1029 1031 1032 1050 1230\n",
      "1031 831 1011 1029 1030 1032 1033 1050 1051 1052 1230 1231 1232 1250 1252\n",
      "1032 811 813 831 832 833 1011 1012 1013 1030 1031 1033 1034 1052 1232\n",
      "1033 833 1013 1031 1032 1034 1035 1052 1053 1054 1232 1233 1234 1252 1254\n",
      "1034 813 815 833 834 835 1013 1014 1015 1032 1033 1035 1036 1054 1234\n",
      "1035 835 1015 1033 1034 1036 1037 1054 1055 1056 1234 1235 1236 1254 1256\n",
      "1036 815 817 835 836 837 1015 1016 1017 1034 1035 1037 1038 1056 1236\n",
      "1037 837 1017 1035 1036 1038 1039 1056 1057 1058 1236 1237 1238 1256 1258\n",
      "1038 817 819 837 838 839 1017 1018 1019 1020 1036 1037 1039 1058 1238\n",
      "1039 839 1019 1020 1021 1037 1038 1040 1058 1059 1220 1238 1239 1240 1258\n",
      "1040 821 839 840 841 859 1020 1021 1039 1041 1042 1058 1059 1060 1240\n",
      "1041 841 1021 1040 1042 1043 1059 1060 1061 1062 1240 1241 1242 1260 1262\n",
      "1042 821 823 841 842 843 1021 1022 1023 1040 1041 1043 1044 1062 1242\n",
      "1043 843 1023 1041 1042 1044 1045 1062 1063 1064 1242 1243 1244 1262 1264\n",
      "1044 823 825 843 844 845 1023 1024 1025 1042 1043 1045 1046 1064 1244\n",
      "1045 845 1025 1043 1044 1046 1047 1064 1065 1066 1244 1245 1246 1264 1266\n",
      "1046 825 827 845 846 847 1025 1026 1027 1044 1045 1047 1048 1066 1246\n",
      "1047 847 1027 1045 1046 1048 1049 1066 1067 1068 1246 1247 1248 1266 1268\n",
      "1048 827 829 847 848 849 1027 1028 1029 1046 1047 1049 1050 1068 1248\n",
      "1049 849 1029 1047 1048 1050 1051 1068 1069 1070 1248 1249 1250 1268 1270\n",
      "1050 829 831 849 850 851 1029 1030 1031 1048 1049 1051 1052 1070 1250\n",
      "1051 851 1031 1049 1050 1052 1053 1070 1071 1072 1250 1251 1252 1270 1272\n",
      "1052 831 833 851 852 853 1031 1032 1033 1050 1051 1053 1054 1072 1252\n",
      "1053 853 1033 1051 1052 1054 1055 1072 1073 1074 1252 1253 1254 1272 1274\n",
      "1054 833 835 853 854 855 1033 1034 1035 1052 1053 1055 1056 1074 1254\n",
      "1055 855 1035 1053 1054 1056 1057 1074 1075 1076 1254 1255 1256 1274 1276\n",
      "1056 835 837 855 856 857 1035 1036 1037 1054 1055 1057 1058 1076 1256\n",
      "1057 857 1037 1055 1056 1058 1059 1076 1077 1078 1256 1257 1258 1276 1278\n",
      "1058 837 839 857 858 859 1037 1038 1039 1040 1056 1057 1059 1078 1258\n",
      "1059 859 1039 1040 1041 1057 1058 1060 1078 1079 1240 1258 1259 1260 1278\n",
      "1060 841 859 860 861 879 1040 1041 1059 1061 1062 1078 1079 1080 1260\n",
      "1061 861 1041 1060 1062 1063 1079 1080 1081 1082 1260 1261 1262 1280 1282\n",
      "1062 841 843 861 862 863 1041 1042 1043 1060 1061 1063 1064 1082 1262\n",
      "1063 863 1043 1061 1062 1064 1065 1082 1083 1084 1262 1263 1264 1282 1284\n",
      "1064 843 845 863 864 865 1043 1044 1045 1062 1063 1065 1066 1084 1264\n",
      "1065 865 1045 1063 1064 1066 1067 1084 1085 1086 1264 1265 1266 1284 1286\n",
      "1066 845 847 865 866 867 1045 1046 1047 1064 1065 1067 1068 1086 1266\n",
      "1067 867 1047 1065 1066 1068 1069 1086 1087 1088 1266 1267 1268 1286 1288\n",
      "1068 847 849 867 868 869 1047 1048 1049 1066 1067 1069 1070 1088 1268\n",
      "1069 869 1049 1067 1068 1070 1071 1088 1089 1090 1268 1269 1270 1288 1290\n",
      "1070 849 851 869 870 871 1049 1050 1051 1068 1069 1071 1072 1090 1270\n",
      "1071 871 1051 1069 1070 1072 1073 1090 1091 1092 1270 1271 1272 1290 1292\n",
      "1072 851 853 871 872 873 1051 1052 1053 1070 1071 1073 1074 1092 1272\n",
      "1073 873 1053 1071 1072 1074 1075 1092 1093 1094 1272 1273 1274 1292 1294\n",
      "1074 853 855 873 874 875 1053 1054 1055 1072 1073 1075 1076 1094 1274\n",
      "1075 875 1055 1073 1074 1076 1077 1094 1095 1096 1274 1275 1276 1294 1296\n",
      "1076 855 857 875 876 877 1055 1056 1057 1074 1075 1077 1078 1096 1276\n",
      "1077 877 1057 1075 1076 1078 1079 1096 1097 1098 1276 1277 1278 1296 1298\n",
      "1078 857 859 877 878 879 1057 1058 1059 1060 1076 1077 1079 1098 1278\n",
      "1079 879 1059 1060 1061 1077 1078 1080 1098 1099 1260 1278 1279 1280 1298\n",
      "1080 861 879 880 881 899 1060 1061 1079 1081 1082 1098 1099 1100 1280\n",
      "1081 881 1061 1080 1082 1083 1099 1100 1101 1102 1280 1281 1282 1300 1302\n",
      "1082 861 863 881 882 883 1061 1062 1063 1080 1081 1083 1084 1102 1282\n",
      "1083 883 1063 1081 1082 1084 1085 1102 1103 1104 1282 1283 1284 1302 1304\n",
      "1084 863 865 883 884 885 1063 1064 1065 1082 1083 1085 1086 1104 1284\n",
      "1085 885 1065 1083 1084 1086 1087 1104 1105 1106 1284 1285 1286 1304 1306\n",
      "1086 865 867 885 886 887 1065 1066 1067 1084 1085 1087 1088 1106 1286\n",
      "1087 887 1067 1085 1086 1088 1089 1106 1107 1108 1286 1287 1288 1306 1308\n",
      "1088 867 869 887 888 889 1067 1068 1069 1086 1087 1089 1090 1108 1288\n",
      "1089 889 1069 1087 1088 1090 1091 1108 1109 1110 1288 1289 1290 1308 1310\n",
      "1090 869 871 889 890 891 1069 1070 1071 1088 1089 1091 1092 1110 1290\n",
      "1091 891 1071 1089 1090 1092 1093 1110 1111 1112 1290 1291 1292 1310 1312\n",
      "1092 871 873 891 892 893 1071 1072 1073 1090 1091 1093 1094 1112 1292\n",
      "1093 893 1073 1091 1092 1094 1095 1112 1113 1114 1292 1293 1294 1312 1314\n",
      "1094 873 875 893 894 895 1073 1074 1075 1092 1093 1095 1096 1114 1294\n",
      "1095 895 1075 1093 1094 1096 1097 1114 1115 1116 1294 1295 1296 1314 1316\n",
      "1096 875 877 895 896 897 1075 1076 1077 1094 1095 1097 1098 1116 1296\n",
      "1097 897 1077 1095 1096 1098 1099 1116 1117 1118 1296 1297 1298 1316 1318\n",
      "1098 877 879 897 898 899 1077 1078 1079 1080 1096 1097 1099 1118 1298\n",
      "1099 899 1079 1080 1081 1097 1098 1100 1118 1119 1280 1298 1299 1300 1318\n",
      "1100 881 899 900 901 919 1080 1081 1099 1101 1102 1118 1119 1120 1300\n",
      "1101 901 1081 1100 1102 1103 1119 1120 1121 1122 1300 1301 1302 1320 1322\n",
      "1102 881 883 901 902 903 1081 1082 1083 1100 1101 1103 1104 1122 1302\n",
      "1103 903 1083 1101 1102 1104 1105 1122 1123 1124 1302 1303 1304 1322 1324\n",
      "1104 883 885 903 904 905 1083 1084 1085 1102 1103 1105 1106 1124 1304\n",
      "1105 905 1085 1103 1104 1106 1107 1124 1125 1126 1304 1305 1306 1324 1326\n",
      "1106 885 887 905 906 907 1085 1086 1087 1104 1105 1107 1108 1126 1306\n",
      "1107 907 1087 1105 1106 1108 1109 1126 1127 1128 1306 1307 1308 1326 1328\n",
      "1108 887 889 907 908 909 1087 1088 1089 1106 1107 1109 1110 1128 1308\n",
      "1109 909 1089 1107 1108 1110 1111 1128 1129 1130 1308 1309 1310 1328 1330\n",
      "1110 889 891 909 910 911 1089 1090 1091 1108 1109 1111 1112 1130 1310\n",
      "1111 911 1091 1109 1110 1112 1113 1130 1131 1132 1310 1311 1312 1330 1332\n",
      "1112 891 893 911 912 913 1091 1092 1093 1110 1111 1113 1114 1132 1312\n",
      "1113 913 1093 1111 1112 1114 1115 1132 1133 1134 1312 1313 1314 1332 1334\n",
      "1114 893 895 913 914 915 1093 1094 1095 1112 1113 1115 1116 1134 1314\n",
      "1115 915 1095 1113 1114 1116 1117 1134 1135 1136 1314 1315 1316 1334 1336\n",
      "1116 895 897 915 916 917 1095 1096 1097 1114 1115 1117 1118 1136 1316\n",
      "1117 917 1097 1115 1116 1118 1119 1136 1137 1138 1316 1317 1318 1336 1338\n",
      "1118 897 899 917 918 919 1097 1098 1099 1100 1116 1117 1119 1138 1318\n",
      "1119 919 1099 1100 1101 1117 1118 1120 1138 1139 1300 1318 1319 1320 1338\n",
      "1120 901 919 920 921 939 1100 1101 1119 1121 1122 1138 1139 1140 1320\n",
      "1121 921 1101 1120 1122 1123 1139 1140 1141 1142 1320 1321 1322 1340 1342\n",
      "1122 901 903 921 922 923 1101 1102 1103 1120 1121 1123 1124 1142 1322\n",
      "1123 923 1103 1121 1122 1124 1125 1142 1143 1144 1322 1323 1324 1342 1344\n",
      "1124 903 905 923 924 925 1103 1104 1105 1122 1123 1125 1126 1144 1324\n",
      "1125 925 1105 1123 1124 1126 1127 1144 1145 1146 1324 1325 1326 1344 1346\n",
      "1126 905 907 925 926 927 1105 1106 1107 1124 1125 1127 1128 1146 1326\n",
      "1127 927 1107 1125 1126 1128 1129 1146 1147 1148 1326 1327 1328 1346 1348\n",
      "1128 907 909 927 928 929 1107 1108 1109 1126 1127 1129 1130 1148 1328\n",
      "1129 929 1109 1127 1128 1130 1131 1148 1149 1150 1328 1329 1330 1348 1350\n",
      "1130 909 911 929 930 931 1109 1110 1111 1128 1129 1131 1132 1150 1330\n",
      "1131 931 1111 1129 1130 1132 1133 1150 1151 1152 1330 1331 1332 1350 1352\n",
      "1132 911 913 931 932 933 1111 1112 1113 1130 1131 1133 1134 1152 1332\n",
      "1133 933 1113 1131 1132 1134 1135 1152 1153 1154 1332 1333 1334 1352 1354\n",
      "1134 913 915 933 934 935 1113 1114 1115 1132 1133 1135 1136 1154 1334\n",
      "1135 935 1115 1133 1134 1136 1137 1154 1155 1156 1334 1335 1336 1354 1356\n",
      "1136 915 917 935 936 937 1115 1116 1117 1134 1135 1137 1138 1156 1336\n",
      "1137 937 1117 1135 1136 1138 1139 1156 1157 1158 1336 1337 1338 1356 1358\n",
      "1138 917 919 937 938 939 1117 1118 1119 1120 1136 1137 1139 1158 1338\n",
      "1139 939 1119 1120 1121 1137 1138 1140 1158 1159 1320 1338 1339 1340 1358\n",
      "1140 921 939 940 941 959 1120 1121 1139 1141 1142 1158 1159 1160 1340\n",
      "1141 941 1121 1140 1142 1143 1159 1160 1161 1162 1340 1341 1342 1360 1362\n",
      "1142 921 923 941 942 943 1121 1122 1123 1140 1141 1143 1144 1162 1342\n",
      "1143 943 1123 1141 1142 1144 1145 1162 1163 1164 1342 1343 1344 1362 1364\n",
      "1144 923 925 943 944 945 1123 1124 1125 1142 1143 1145 1146 1164 1344\n",
      "1145 945 1125 1143 1144 1146 1147 1164 1165 1166 1344 1345 1346 1364 1366\n",
      "1146 925 927 945 946 947 1125 1126 1127 1144 1145 1147 1148 1166 1346\n",
      "1147 947 1127 1145 1146 1148 1149 1166 1167 1168 1346 1347 1348 1366 1368\n",
      "1148 927 929 947 948 949 1127 1128 1129 1146 1147 1149 1150 1168 1348\n",
      "1149 949 1129 1147 1148 1150 1151 1168 1169 1170 1348 1349 1350 1368 1370\n",
      "1150 929 931 949 950 951 1129 1130 1131 1148 1149 1151 1152 1170 1350\n",
      "1151 951 1131 1149 1150 1152 1153 1170 1171 1172 1350 1351 1352 1370 1372\n",
      "1152 931 933 951 952 953 1131 1132 1133 1150 1151 1153 1154 1172 1352\n",
      "1153 953 1133 1151 1152 1154 1155 1172 1173 1174 1352 1353 1354 1372 1374\n",
      "1154 933 935 953 954 955 1133 1134 1135 1152 1153 1155 1156 1174 1354\n",
      "1155 955 1135 1153 1154 1156 1157 1174 1175 1176 1354 1355 1356 1374 1376\n",
      "1156 935 937 955 956 957 1135 1136 1137 1154 1155 1157 1158 1176 1356\n",
      "1157 957 1137 1155 1156 1158 1159 1176 1177 1178 1356 1357 1358 1376 1378\n",
      "1158 937 939 957 958 959 1137 1138 1139 1140 1156 1157 1159 1178 1358\n",
      "1159 959 1139 1140 1141 1157 1158 1160 1178 1179 1340 1358 1359 1360 1378\n",
      "1160 941 959 960 961 979 1140 1141 1159 1161 1162 1178 1179 1180 1360\n",
      "1161 961 1141 1160 1162 1163 1179 1180 1181 1182 1360 1361 1362 1380 1382\n",
      "1162 941 943 961 962 963 1141 1142 1143 1160 1161 1163 1164 1182 1362\n",
      "1163 963 1143 1161 1162 1164 1165 1182 1183 1184 1362 1363 1364 1382 1384\n",
      "1164 943 945 963 964 965 1143 1144 1145 1162 1163 1165 1166 1184 1364\n",
      "1165 965 1145 1163 1164 1166 1167 1184 1185 1186 1364 1365 1366 1384 1386\n",
      "1166 945 947 965 966 967 1145 1146 1147 1164 1165 1167 1168 1186 1366\n",
      "1167 967 1147 1165 1166 1168 1169 1186 1187 1188 1366 1367 1368 1386 1388\n",
      "1168 947 949 967 968 969 1147 1148 1149 1166 1167 1169 1170 1188 1368\n",
      "1169 969 1149 1167 1168 1170 1171 1188 1189 1190 1368 1369 1370 1388 1390\n",
      "1170 949 951 969 970 971 1149 1150 1151 1168 1169 1171 1172 1190 1370\n",
      "1171 971 1151 1169 1170 1172 1173 1190 1191 1192 1370 1371 1372 1390 1392\n",
      "1172 951 953 971 972 973 1151 1152 1153 1170 1171 1173 1174 1192 1372\n",
      "1173 973 1153 1171 1172 1174 1175 1192 1193 1194 1372 1373 1374 1392 1394\n",
      "1174 953 955 973 974 975 1153 1154 1155 1172 1173 1175 1176 1194 1374\n",
      "1175 975 1155 1173 1174 1176 1177 1194 1195 1196 1374 1375 1376 1394 1396\n",
      "1176 955 957 975 976 977 1155 1156 1157 1174 1175 1177 1178 1196 1376\n",
      "1177 977 1157 1175 1176 1178 1179 1196 1197 1198 1376 1377 1378 1396 1398\n",
      "1178 957 959 977 978 979 1157 1158 1159 1160 1176 1177 1179 1198 1378\n",
      "1179 979 1159 1160 1161 1177 1178 1180 1198 1199 1360 1378 1379 1380 1398\n",
      "1180 961 979 980 981 999 1000 1160 1161 1179 1181 1182 1198 1199 1380\n",
      "1181 981 1000 1001 1002 1161 1180 1182 1183 1199 1200 1202 1380 1381 1382\n",
      "1182 961 963 981 982 983 1002 1161 1162 1163 1180 1181 1183 1184 1382\n",
      "1183 983 1002 1003 1004 1163 1181 1182 1184 1185 1202 1204 1382 1383 1384\n",
      "1184 963 965 983 984 985 1004 1163 1164 1165 1182 1183 1185 1186 1384\n",
      "1185 985 1004 1005 1006 1165 1183 1184 1186 1187 1204 1206 1384 1385 1386\n",
      "1186 965 967 985 986 987 1006 1165 1166 1167 1184 1185 1187 1188 1386\n",
      "1187 987 1006 1007 1008 1167 1185 1186 1188 1189 1206 1208 1386 1387 1388\n",
      "1188 967 969 987 988 989 1008 1167 1168 1169 1186 1187 1189 1190 1388\n",
      "1189 989 1008 1009 1010 1169 1187 1188 1190 1191 1208 1210 1388 1389 1390\n",
      "1190 969 971 989 990 991 1010 1169 1170 1171 1188 1189 1191 1192 1390\n",
      "1191 991 1010 1011 1012 1171 1189 1190 1192 1193 1210 1212 1390 1391 1392\n",
      "1192 971 973 991 992 993 1012 1171 1172 1173 1190 1191 1193 1194 1392\n",
      "1193 993 1012 1013 1014 1173 1191 1192 1194 1195 1212 1214 1392 1393 1394\n",
      "1194 973 975 993 994 995 1014 1173 1174 1175 1192 1193 1195 1196 1394\n",
      "1195 995 1014 1015 1016 1175 1193 1194 1196 1197 1214 1216 1394 1395 1396\n",
      "1196 975 977 995 996 997 1016 1175 1176 1177 1194 1195 1197 1198 1396\n",
      "1197 997 1016 1017 1018 1177 1195 1196 1198 1199 1216 1218 1396 1397 1398\n",
      "1198 977 979 997 998 999 1018 1177 1178 1179 1180 1196 1197 1199 1398\n",
      "1199 999 1000 1018 1019 1179 1180 1181 1197 1198 1200 1218 1380 1398 1399\n",
      "1200 1000 1001 1019 1181 1199 1201 1202 1218 1219 1220 1380 1381 1399 1400\n",
      "1201 1001 1200 1202 1203 1219 1220 1221 1222 1381 1400 1401 1402 1420 1422\n",
      "1202 1001 1002 1003 1181 1183 1200 1201 1203 1204 1222 1381 1382 1383 1402\n",
      "1203 1003 1201 1202 1204 1205 1222 1223 1224 1383 1402 1403 1404 1422 1424\n",
      "1204 1003 1004 1005 1183 1185 1202 1203 1205 1206 1224 1383 1384 1385 1404\n",
      "1205 1005 1203 1204 1206 1207 1224 1225 1226 1385 1404 1405 1406 1424 1426\n",
      "1206 1005 1006 1007 1185 1187 1204 1205 1207 1208 1226 1385 1386 1387 1406\n",
      "1207 1007 1205 1206 1208 1209 1226 1227 1228 1387 1406 1407 1408 1426 1428\n",
      "1208 1007 1008 1009 1187 1189 1206 1207 1209 1210 1228 1387 1388 1389 1408\n",
      "1209 1009 1207 1208 1210 1211 1228 1229 1230 1389 1408 1409 1410 1428 1430\n",
      "1210 1009 1010 1011 1189 1191 1208 1209 1211 1212 1230 1389 1390 1391 1410\n",
      "1211 1011 1209 1210 1212 1213 1230 1231 1232 1391 1410 1411 1412 1430 1432\n",
      "1212 1011 1012 1013 1191 1193 1210 1211 1213 1214 1232 1391 1392 1393 1412\n",
      "1213 1013 1211 1212 1214 1215 1232 1233 1234 1393 1412 1413 1414 1432 1434\n",
      "1214 1013 1014 1015 1193 1195 1212 1213 1215 1216 1234 1393 1394 1395 1414\n",
      "1215 1015 1213 1214 1216 1217 1234 1235 1236 1395 1414 1415 1416 1434 1436\n",
      "1216 1015 1016 1017 1195 1197 1214 1215 1217 1218 1236 1395 1396 1397 1416\n",
      "1217 1017 1215 1216 1218 1219 1236 1237 1238 1397 1416 1417 1418 1436 1438\n",
      "1218 1017 1018 1019 1197 1199 1200 1216 1217 1219 1238 1397 1398 1399 1418\n",
      "1219 1019 1200 1201 1217 1218 1220 1238 1239 1399 1400 1418 1419 1420 1438\n",
      "1220 1001 1019 1020 1021 1039 1200 1201 1219 1221 1222 1238 1239 1240 1420\n",
      "1221 1021 1201 1220 1222 1223 1239 1240 1241 1242 1420 1421 1422 1440 1442\n",
      "1222 1001 1003 1021 1022 1023 1201 1202 1203 1220 1221 1223 1224 1242 1422\n",
      "1223 1023 1203 1221 1222 1224 1225 1242 1243 1244 1422 1423 1424 1442 1444\n",
      "1224 1003 1005 1023 1024 1025 1203 1204 1205 1222 1223 1225 1226 1244 1424\n",
      "1225 1025 1205 1223 1224 1226 1227 1244 1245 1246 1424 1425 1426 1444 1446\n",
      "1226 1005 1007 1025 1026 1027 1205 1206 1207 1224 1225 1227 1228 1246 1426\n",
      "1227 1027 1207 1225 1226 1228 1229 1246 1247 1248 1426 1427 1428 1446 1448\n",
      "1228 1007 1009 1027 1028 1029 1207 1208 1209 1226 1227 1229 1230 1248 1428\n",
      "1229 1029 1209 1227 1228 1230 1231 1248 1249 1250 1428 1429 1430 1448 1450\n",
      "1230 1009 1011 1029 1030 1031 1209 1210 1211 1228 1229 1231 1232 1250 1430\n",
      "1231 1031 1211 1229 1230 1232 1233 1250 1251 1252 1430 1431 1432 1450 1452\n",
      "1232 1011 1013 1031 1032 1033 1211 1212 1213 1230 1231 1233 1234 1252 1432\n",
      "1233 1033 1213 1231 1232 1234 1235 1252 1253 1254 1432 1433 1434 1452 1454\n",
      "1234 1013 1015 1033 1034 1035 1213 1214 1215 1232 1233 1235 1236 1254 1434\n",
      "1235 1035 1215 1233 1234 1236 1237 1254 1255 1256 1434 1435 1436 1454 1456\n",
      "1236 1015 1017 1035 1036 1037 1215 1216 1217 1234 1235 1237 1238 1256 1436\n",
      "1237 1037 1217 1235 1236 1238 1239 1256 1257 1258 1436 1437 1438 1456 1458\n",
      "1238 1017 1019 1037 1038 1039 1217 1218 1219 1220 1236 1237 1239 1258 1438\n",
      "1239 1039 1219 1220 1221 1237 1238 1240 1258 1259 1420 1438 1439 1440 1458\n",
      "1240 1021 1039 1040 1041 1059 1220 1221 1239 1241 1242 1258 1259 1260 1440\n",
      "1241 1041 1221 1240 1242 1243 1259 1260 1261 1262 1440 1441 1442 1460 1462\n",
      "1242 1021 1023 1041 1042 1043 1221 1222 1223 1240 1241 1243 1244 1262 1442\n",
      "1243 1043 1223 1241 1242 1244 1245 1262 1263 1264 1442 1443 1444 1462 1464\n",
      "1244 1023 1025 1043 1044 1045 1223 1224 1225 1242 1243 1245 1246 1264 1444\n",
      "1245 1045 1225 1243 1244 1246 1247 1264 1265 1266 1444 1445 1446 1464 1466\n",
      "1246 1025 1027 1045 1046 1047 1225 1226 1227 1244 1245 1247 1248 1266 1446\n",
      "1247 1047 1227 1245 1246 1248 1249 1266 1267 1268 1446 1447 1448 1466 1468\n",
      "1248 1027 1029 1047 1048 1049 1227 1228 1229 1246 1247 1249 1250 1268 1448\n",
      "1249 1049 1229 1247 1248 1250 1251 1268 1269 1270 1448 1449 1450 1468 1470\n",
      "1250 1029 1031 1049 1050 1051 1229 1230 1231 1248 1249 1251 1252 1270 1450\n",
      "1251 1051 1231 1249 1250 1252 1253 1270 1271 1272 1450 1451 1452 1470 1472\n",
      "1252 1031 1033 1051 1052 1053 1231 1232 1233 1250 1251 1253 1254 1272 1452\n",
      "1253 1053 1233 1251 1252 1254 1255 1272 1273 1274 1452 1453 1454 1472 1474\n",
      "1254 1033 1035 1053 1054 1055 1233 1234 1235 1252 1253 1255 1256 1274 1454\n",
      "1255 1055 1235 1253 1254 1256 1257 1274 1275 1276 1454 1455 1456 1474 1476\n",
      "1256 1035 1037 1055 1056 1057 1235 1236 1237 1254 1255 1257 1258 1276 1456\n",
      "1257 1057 1237 1255 1256 1258 1259 1276 1277 1278 1456 1457 1458 1476 1478\n",
      "1258 1037 1039 1057 1058 1059 1237 1238 1239 1240 1256 1257 1259 1278 1458\n",
      "1259 1059 1239 1240 1241 1257 1258 1260 1278 1279 1440 1458 1459 1460 1478\n",
      "1260 1041 1059 1060 1061 1079 1240 1241 1259 1261 1262 1278 1279 1280 1460\n",
      "1261 1061 1241 1260 1262 1263 1279 1280 1281 1282 1460 1461 1462 1480 1482\n",
      "1262 1041 1043 1061 1062 1063 1241 1242 1243 1260 1261 1263 1264 1282 1462\n",
      "1263 1063 1243 1261 1262 1264 1265 1282 1283 1284 1462 1463 1464 1482 1484\n",
      "1264 1043 1045 1063 1064 1065 1243 1244 1245 1262 1263 1265 1266 1284 1464\n",
      "1265 1065 1245 1263 1264 1266 1267 1284 1285 1286 1464 1465 1466 1484 1486\n",
      "1266 1045 1047 1065 1066 1067 1245 1246 1247 1264 1265 1267 1268 1286 1466\n",
      "1267 1067 1247 1265 1266 1268 1269 1286 1287 1288 1466 1467 1468 1486 1488\n",
      "1268 1047 1049 1067 1068 1069 1247 1248 1249 1266 1267 1269 1270 1288 1468\n",
      "1269 1069 1249 1267 1268 1270 1271 1288 1289 1290 1468 1469 1470 1488 1490\n",
      "1270 1049 1051 1069 1070 1071 1249 1250 1251 1268 1269 1271 1272 1290 1470\n",
      "1271 1071 1251 1269 1270 1272 1273 1290 1291 1292 1470 1471 1472 1490 1492\n",
      "1272 1051 1053 1071 1072 1073 1251 1252 1253 1270 1271 1273 1274 1292 1472\n",
      "1273 1073 1253 1271 1272 1274 1275 1292 1293 1294 1472 1473 1474 1492 1494\n",
      "1274 1053 1055 1073 1074 1075 1253 1254 1255 1272 1273 1275 1276 1294 1474\n",
      "1275 1075 1255 1273 1274 1276 1277 1294 1295 1296 1474 1475 1476 1494 1496\n",
      "1276 1055 1057 1075 1076 1077 1255 1256 1257 1274 1275 1277 1278 1296 1476\n",
      "1277 1077 1257 1275 1276 1278 1279 1296 1297 1298 1476 1477 1478 1496 1498\n",
      "1278 1057 1059 1077 1078 1079 1257 1258 1259 1260 1276 1277 1279 1298 1478\n",
      "1279 1079 1259 1260 1261 1277 1278 1280 1298 1299 1460 1478 1479 1480 1498\n",
      "1280 1061 1079 1080 1081 1099 1260 1261 1279 1281 1282 1298 1299 1300 1480\n",
      "1281 1081 1261 1280 1282 1283 1299 1300 1301 1302 1480 1481 1482 1500 1502\n",
      "1282 1061 1063 1081 1082 1083 1261 1262 1263 1280 1281 1283 1284 1302 1482\n",
      "1283 1083 1263 1281 1282 1284 1285 1302 1303 1304 1482 1483 1484 1502 1504\n",
      "1284 1063 1065 1083 1084 1085 1263 1264 1265 1282 1283 1285 1286 1304 1484\n",
      "1285 1085 1265 1283 1284 1286 1287 1304 1305 1306 1484 1485 1486 1504 1506\n",
      "1286 1065 1067 1085 1086 1087 1265 1266 1267 1284 1285 1287 1288 1306 1486\n",
      "1287 1087 1267 1285 1286 1288 1289 1306 1307 1308 1486 1487 1488 1506 1508\n",
      "1288 1067 1069 1087 1088 1089 1267 1268 1269 1286 1287 1289 1290 1308 1488\n",
      "1289 1089 1269 1287 1288 1290 1291 1308 1309 1310 1488 1489 1490 1508 1510\n",
      "1290 1069 1071 1089 1090 1091 1269 1270 1271 1288 1289 1291 1292 1310 1490\n",
      "1291 1091 1271 1289 1290 1292 1293 1310 1311 1312 1490 1491 1492 1510 1512\n",
      "1292 1071 1073 1091 1092 1093 1271 1272 1273 1290 1291 1293 1294 1312 1492\n",
      "1293 1093 1273 1291 1292 1294 1295 1312 1313 1314 1492 1493 1494 1512 1514\n",
      "1294 1073 1075 1093 1094 1095 1273 1274 1275 1292 1293 1295 1296 1314 1494\n",
      "1295 1095 1275 1293 1294 1296 1297 1314 1315 1316 1494 1495 1496 1514 1516\n",
      "1296 1075 1077 1095 1096 1097 1275 1276 1277 1294 1295 1297 1298 1316 1496\n",
      "1297 1097 1277 1295 1296 1298 1299 1316 1317 1318 1496 1497 1498 1516 1518\n",
      "1298 1077 1079 1097 1098 1099 1277 1278 1279 1280 1296 1297 1299 1318 1498\n",
      "1299 1099 1279 1280 1281 1297 1298 1300 1318 1319 1480 1498 1499 1500 1518\n",
      "1300 1081 1099 1100 1101 1119 1280 1281 1299 1301 1302 1318 1319 1320 1500\n",
      "1301 1101 1281 1300 1302 1303 1319 1320 1321 1322 1500 1501 1502 1520 1522\n",
      "1302 1081 1083 1101 1102 1103 1281 1282 1283 1300 1301 1303 1304 1322 1502\n",
      "1303 1103 1283 1301 1302 1304 1305 1322 1323 1324 1502 1503 1504 1522 1524\n",
      "1304 1083 1085 1103 1104 1105 1283 1284 1285 1302 1303 1305 1306 1324 1504\n",
      "1305 1105 1285 1303 1304 1306 1307 1324 1325 1326 1504 1505 1506 1524 1526\n",
      "1306 1085 1087 1105 1106 1107 1285 1286 1287 1304 1305 1307 1308 1326 1506\n",
      "1307 1107 1287 1305 1306 1308 1309 1326 1327 1328 1506 1507 1508 1526 1528\n",
      "1308 1087 1089 1107 1108 1109 1287 1288 1289 1306 1307 1309 1310 1328 1508\n",
      "1309 1109 1289 1307 1308 1310 1311 1328 1329 1330 1508 1509 1510 1528 1530\n",
      "1310 1089 1091 1109 1110 1111 1289 1290 1291 1308 1309 1311 1312 1330 1510\n",
      "1311 1111 1291 1309 1310 1312 1313 1330 1331 1332 1510 1511 1512 1530 1532\n",
      "1312 1091 1093 1111 1112 1113 1291 1292 1293 1310 1311 1313 1314 1332 1512\n",
      "1313 1113 1293 1311 1312 1314 1315 1332 1333 1334 1512 1513 1514 1532 1534\n",
      "1314 1093 1095 1113 1114 1115 1293 1294 1295 1312 1313 1315 1316 1334 1514\n",
      "1315 1115 1295 1313 1314 1316 1317 1334 1335 1336 1514 1515 1516 1534 1536\n",
      "1316 1095 1097 1115 1116 1117 1295 1296 1297 1314 1315 1317 1318 1336 1516\n",
      "1317 1117 1297 1315 1316 1318 1319 1336 1337 1338 1516 1517 1518 1536 1538\n",
      "1318 1097 1099 1117 1118 1119 1297 1298 1299 1300 1316 1317 1319 1338 1518\n",
      "1319 1119 1299 1300 1301 1317 1318 1320 1338 1339 1500 1518 1519 1520 1538\n",
      "1320 1101 1119 1120 1121 1139 1300 1301 1319 1321 1322 1338 1339 1340 1520\n",
      "1321 1121 1301 1320 1322 1323 1339 1340 1341 1342 1520 1521 1522 1540 1542\n",
      "1322 1101 1103 1121 1122 1123 1301 1302 1303 1320 1321 1323 1324 1342 1522\n",
      "1323 1123 1303 1321 1322 1324 1325 1342 1343 1344 1522 1523 1524 1542 1544\n",
      "1324 1103 1105 1123 1124 1125 1303 1304 1305 1322 1323 1325 1326 1344 1524\n",
      "1325 1125 1305 1323 1324 1326 1327 1344 1345 1346 1524 1525 1526 1544 1546\n",
      "1326 1105 1107 1125 1126 1127 1305 1306 1307 1324 1325 1327 1328 1346 1526\n",
      "1327 1127 1307 1325 1326 1328 1329 1346 1347 1348 1526 1527 1528 1546 1548\n",
      "1328 1107 1109 1127 1128 1129 1307 1308 1309 1326 1327 1329 1330 1348 1528\n",
      "1329 1129 1309 1327 1328 1330 1331 1348 1349 1350 1528 1529 1530 1548 1550\n",
      "1330 1109 1111 1129 1130 1131 1309 1310 1311 1328 1329 1331 1332 1350 1530\n",
      "1331 1131 1311 1329 1330 1332 1333 1350 1351 1352 1530 1531 1532 1550 1552\n",
      "1332 1111 1113 1131 1132 1133 1311 1312 1313 1330 1331 1333 1334 1352 1532\n",
      "1333 1133 1313 1331 1332 1334 1335 1352 1353 1354 1532 1533 1534 1552 1554\n",
      "1334 1113 1115 1133 1134 1135 1313 1314 1315 1332 1333 1335 1336 1354 1534\n",
      "1335 1135 1315 1333 1334 1336 1337 1354 1355 1356 1534 1535 1536 1554 1556\n",
      "1336 1115 1117 1135 1136 1137 1315 1316 1317 1334 1335 1337 1338 1356 1536\n",
      "1337 1137 1317 1335 1336 1338 1339 1356 1357 1358 1536 1537 1538 1556 1558\n",
      "1338 1117 1119 1137 1138 1139 1317 1318 1319 1320 1336 1337 1339 1358 1538\n",
      "1339 1139 1319 1320 1321 1337 1338 1340 1358 1359 1520 1538 1539 1540 1558\n",
      "1340 1121 1139 1140 1141 1159 1320 1321 1339 1341 1342 1358 1359 1360 1540\n",
      "1341 1141 1321 1340 1342 1343 1359 1360 1361 1362 1540 1541 1542 1560 1562\n",
      "1342 1121 1123 1141 1142 1143 1321 1322 1323 1340 1341 1343 1344 1362 1542\n",
      "1343 1143 1323 1341 1342 1344 1345 1362 1363 1364 1542 1543 1544 1562 1564\n",
      "1344 1123 1125 1143 1144 1145 1323 1324 1325 1342 1343 1345 1346 1364 1544\n",
      "1345 1145 1325 1343 1344 1346 1347 1364 1365 1366 1544 1545 1546 1564 1566\n",
      "1346 1125 1127 1145 1146 1147 1325 1326 1327 1344 1345 1347 1348 1366 1546\n",
      "1347 1147 1327 1345 1346 1348 1349 1366 1367 1368 1546 1547 1548 1566 1568\n",
      "1348 1127 1129 1147 1148 1149 1327 1328 1329 1346 1347 1349 1350 1368 1548\n",
      "1349 1149 1329 1347 1348 1350 1351 1368 1369 1370 1548 1549 1550 1568 1570\n",
      "1350 1129 1131 1149 1150 1151 1329 1330 1331 1348 1349 1351 1352 1370 1550\n",
      "1351 1151 1331 1349 1350 1352 1353 1370 1371 1372 1550 1551 1552 1570 1572\n",
      "1352 1131 1133 1151 1152 1153 1331 1332 1333 1350 1351 1353 1354 1372 1552\n",
      "1353 1153 1333 1351 1352 1354 1355 1372 1373 1374 1552 1553 1554 1572 1574\n",
      "1354 1133 1135 1153 1154 1155 1333 1334 1335 1352 1353 1355 1356 1374 1554\n",
      "1355 1155 1335 1353 1354 1356 1357 1374 1375 1376 1554 1555 1556 1574 1576\n",
      "1356 1135 1137 1155 1156 1157 1335 1336 1337 1354 1355 1357 1358 1376 1556\n",
      "1357 1157 1337 1355 1356 1358 1359 1376 1377 1378 1556 1557 1558 1576 1578\n",
      "1358 1137 1139 1157 1158 1159 1337 1338 1339 1340 1356 1357 1359 1378 1558\n",
      "1359 1159 1339 1340 1341 1357 1358 1360 1378 1379 1540 1558 1559 1560 1578\n",
      "1360 1141 1159 1160 1161 1179 1340 1341 1359 1361 1362 1378 1379 1380 1560\n",
      "1361 1161 1341 1360 1362 1363 1379 1380 1381 1382 1560 1561 1562 1580 1582\n",
      "1362 1141 1143 1161 1162 1163 1341 1342 1343 1360 1361 1363 1364 1382 1562\n",
      "1363 1163 1343 1361 1362 1364 1365 1382 1383 1384 1562 1563 1564 1582 1584\n",
      "1364 1143 1145 1163 1164 1165 1343 1344 1345 1362 1363 1365 1366 1384 1564\n",
      "1365 1165 1345 1363 1364 1366 1367 1384 1385 1386 1564 1565 1566 1584 1586\n",
      "1366 1145 1147 1165 1166 1167 1345 1346 1347 1364 1365 1367 1368 1386 1566\n",
      "1367 1167 1347 1365 1366 1368 1369 1386 1387 1388 1566 1567 1568 1586 1588\n",
      "1368 1147 1149 1167 1168 1169 1347 1348 1349 1366 1367 1369 1370 1388 1568\n",
      "1369 1169 1349 1367 1368 1370 1371 1388 1389 1390 1568 1569 1570 1588 1590\n",
      "1370 1149 1151 1169 1170 1171 1349 1350 1351 1368 1369 1371 1372 1390 1570\n",
      "1371 1171 1351 1369 1370 1372 1373 1390 1391 1392 1570 1571 1572 1590 1592\n",
      "1372 1151 1153 1171 1172 1173 1351 1352 1353 1370 1371 1373 1374 1392 1572\n",
      "1373 1173 1353 1371 1372 1374 1375 1392 1393 1394 1572 1573 1574 1592 1594\n",
      "1374 1153 1155 1173 1174 1175 1353 1354 1355 1372 1373 1375 1376 1394 1574\n",
      "1375 1175 1355 1373 1374 1376 1377 1394 1395 1396 1574 1575 1576 1594 1596\n",
      "1376 1155 1157 1175 1176 1177 1355 1356 1357 1374 1375 1377 1378 1396 1576\n",
      "1377 1177 1357 1375 1376 1378 1379 1396 1397 1398 1576 1577 1578 1596 1598\n",
      "1378 1157 1159 1177 1178 1179 1357 1358 1359 1360 1376 1377 1379 1398 1578\n",
      "1379 1179 1359 1360 1361 1377 1378 1380 1398 1399 1560 1578 1579 1580 1598\n",
      "1380 1161 1179 1180 1181 1199 1200 1360 1361 1379 1381 1382 1398 1399 1580\n",
      "1381 1181 1200 1201 1202 1361 1380 1382 1383 1399 1400 1402 1580 1581 1582\n",
      "1382 1161 1163 1181 1182 1183 1202 1361 1362 1363 1380 1381 1383 1384 1582\n",
      "1383 1183 1202 1203 1204 1363 1381 1382 1384 1385 1402 1404 1582 1583 1584\n",
      "1384 1163 1165 1183 1184 1185 1204 1363 1364 1365 1382 1383 1385 1386 1584\n",
      "1385 1185 1204 1205 1206 1365 1383 1384 1386 1387 1404 1406 1584 1585 1586\n",
      "1386 1165 1167 1185 1186 1187 1206 1365 1366 1367 1384 1385 1387 1388 1586\n",
      "1387 1187 1206 1207 1208 1367 1385 1386 1388 1389 1406 1408 1586 1587 1588\n",
      "1388 1167 1169 1187 1188 1189 1208 1367 1368 1369 1386 1387 1389 1390 1588\n",
      "1389 1189 1208 1209 1210 1369 1387 1388 1390 1391 1408 1410 1588 1589 1590\n",
      "1390 1169 1171 1189 1190 1191 1210 1369 1370 1371 1388 1389 1391 1392 1590\n",
      "1391 1191 1210 1211 1212 1371 1389 1390 1392 1393 1410 1412 1590 1591 1592\n",
      "1392 1171 1173 1191 1192 1193 1212 1371 1372 1373 1390 1391 1393 1394 1592\n",
      "1393 1193 1212 1213 1214 1373 1391 1392 1394 1395 1412 1414 1592 1593 1594\n",
      "1394 1173 1175 1193 1194 1195 1214 1373 1374 1375 1392 1393 1395 1396 1594\n",
      "1395 1195 1214 1215 1216 1375 1393 1394 1396 1397 1414 1416 1594 1595 1596\n",
      "1396 1175 1177 1195 1196 1197 1216 1375 1376 1377 1394 1395 1397 1398 1596\n",
      "1397 1197 1216 1217 1218 1377 1395 1396 1398 1399 1416 1418 1596 1597 1598\n",
      "1398 1177 1179 1197 1198 1199 1218 1377 1378 1379 1380 1396 1397 1399 1598\n",
      "1399 1199 1200 1218 1219 1379 1380 1381 1397 1398 1400 1418 1580 1598 1599\n",
      "1400 1200 1201 1219 1381 1399 1401 1402 1418 1419 1420 1580 1581 1599 1600\n",
      "1401 1201 1400 1402 1403 1419 1420 1421 1422 1581 1600 1601 1602 1620 1622\n",
      "1402 1201 1202 1203 1381 1383 1400 1401 1403 1404 1422 1581 1582 1583 1602\n",
      "1403 1203 1401 1402 1404 1405 1422 1423 1424 1583 1602 1603 1604 1622 1624\n",
      "1404 1203 1204 1205 1383 1385 1402 1403 1405 1406 1424 1583 1584 1585 1604\n",
      "1405 1205 1403 1404 1406 1407 1424 1425 1426 1585 1604 1605 1606 1624 1626\n",
      "1406 1205 1206 1207 1385 1387 1404 1405 1407 1408 1426 1585 1586 1587 1606\n",
      "1407 1207 1405 1406 1408 1409 1426 1427 1428 1587 1606 1607 1608 1626 1628\n",
      "1408 1207 1208 1209 1387 1389 1406 1407 1409 1410 1428 1587 1588 1589 1608\n",
      "1409 1209 1407 1408 1410 1411 1428 1429 1430 1589 1608 1609 1610 1628 1630\n",
      "1410 1209 1210 1211 1389 1391 1408 1409 1411 1412 1430 1589 1590 1591 1610\n",
      "1411 1211 1409 1410 1412 1413 1430 1431 1432 1591 1610 1611 1612 1630 1632\n",
      "1412 1211 1212 1213 1391 1393 1410 1411 1413 1414 1432 1591 1592 1593 1612\n",
      "1413 1213 1411 1412 1414 1415 1432 1433 1434 1593 1612 1613 1614 1632 1634\n",
      "1414 1213 1214 1215 1393 1395 1412 1413 1415 1416 1434 1593 1594 1595 1614\n",
      "1415 1215 1413 1414 1416 1417 1434 1435 1436 1595 1614 1615 1616 1634 1636\n",
      "1416 1215 1216 1217 1395 1397 1414 1415 1417 1418 1436 1595 1596 1597 1616\n",
      "1417 1217 1415 1416 1418 1419 1436 1437 1438 1597 1616 1617 1618 1636 1638\n",
      "1418 1217 1218 1219 1397 1399 1400 1416 1417 1419 1438 1597 1598 1599 1618\n",
      "1419 1219 1400 1401 1417 1418 1420 1438 1439 1599 1600 1618 1619 1620 1638\n",
      "1420 1201 1219 1220 1221 1239 1400 1401 1419 1421 1422 1438 1439 1440 1620\n",
      "1421 1221 1401 1420 1422 1423 1439 1440 1441 1442 1620 1621 1622 1640 1642\n",
      "1422 1201 1203 1221 1222 1223 1401 1402 1403 1420 1421 1423 1424 1442 1622\n",
      "1423 1223 1403 1421 1422 1424 1425 1442 1443 1444 1622 1623 1624 1642 1644\n",
      "1424 1203 1205 1223 1224 1225 1403 1404 1405 1422 1423 1425 1426 1444 1624\n",
      "1425 1225 1405 1423 1424 1426 1427 1444 1445 1446 1624 1625 1626 1644 1646\n",
      "1426 1205 1207 1225 1226 1227 1405 1406 1407 1424 1425 1427 1428 1446 1626\n",
      "1427 1227 1407 1425 1426 1428 1429 1446 1447 1448 1626 1627 1628 1646 1648\n",
      "1428 1207 1209 1227 1228 1229 1407 1408 1409 1426 1427 1429 1430 1448 1628\n",
      "1429 1229 1409 1427 1428 1430 1431 1448 1449 1450 1628 1629 1630 1648 1650\n",
      "1430 1209 1211 1229 1230 1231 1409 1410 1411 1428 1429 1431 1432 1450 1630\n",
      "1431 1231 1411 1429 1430 1432 1433 1450 1451 1452 1630 1631 1632 1650 1652\n",
      "1432 1211 1213 1231 1232 1233 1411 1412 1413 1430 1431 1433 1434 1452 1632\n",
      "1433 1233 1413 1431 1432 1434 1435 1452 1453 1454 1632 1633 1634 1652 1654\n",
      "1434 1213 1215 1233 1234 1235 1413 1414 1415 1432 1433 1435 1436 1454 1634\n",
      "1435 1235 1415 1433 1434 1436 1437 1454 1455 1456 1634 1635 1636 1654 1656\n",
      "1436 1215 1217 1235 1236 1237 1415 1416 1417 1434 1435 1437 1438 1456 1636\n",
      "1437 1237 1417 1435 1436 1438 1439 1456 1457 1458 1636 1637 1638 1656 1658\n",
      "1438 1217 1219 1237 1238 1239 1417 1418 1419 1420 1436 1437 1439 1458 1638\n",
      "1439 1239 1419 1420 1421 1437 1438 1440 1458 1459 1620 1638 1639 1640 1658\n",
      "1440 1221 1239 1240 1241 1259 1420 1421 1439 1441 1442 1458 1459 1460 1640\n",
      "1441 1241 1421 1440 1442 1443 1459 1460 1461 1462 1640 1641 1642 1660 1662\n",
      "1442 1221 1223 1241 1242 1243 1421 1422 1423 1440 1441 1443 1444 1462 1642\n",
      "1443 1243 1423 1441 1442 1444 1445 1462 1463 1464 1642 1643 1644 1662 1664\n",
      "1444 1223 1225 1243 1244 1245 1423 1424 1425 1442 1443 1445 1446 1464 1644\n",
      "1445 1245 1425 1443 1444 1446 1447 1464 1465 1466 1644 1645 1646 1664 1666\n",
      "1446 1225 1227 1245 1246 1247 1425 1426 1427 1444 1445 1447 1448 1466 1646\n",
      "1447 1247 1427 1445 1446 1448 1449 1466 1467 1468 1646 1647 1648 1666 1668\n",
      "1448 1227 1229 1247 1248 1249 1427 1428 1429 1446 1447 1449 1450 1468 1648\n",
      "1449 1249 1429 1447 1448 1450 1451 1468 1469 1470 1648 1649 1650 1668 1670\n",
      "1450 1229 1231 1249 1250 1251 1429 1430 1431 1448 1449 1451 1452 1470 1650\n",
      "1451 1251 1431 1449 1450 1452 1453 1470 1471 1472 1650 1651 1652 1670 1672\n",
      "1452 1231 1233 1251 1252 1253 1431 1432 1433 1450 1451 1453 1454 1472 1652\n",
      "1453 1253 1433 1451 1452 1454 1455 1472 1473 1474 1652 1653 1654 1672 1674\n",
      "1454 1233 1235 1253 1254 1255 1433 1434 1435 1452 1453 1455 1456 1474 1654\n",
      "1455 1255 1435 1453 1454 1456 1457 1474 1475 1476 1654 1655 1656 1674 1676\n",
      "1456 1235 1237 1255 1256 1257 1435 1436 1437 1454 1455 1457 1458 1476 1656\n",
      "1457 1257 1437 1455 1456 1458 1459 1476 1477 1478 1656 1657 1658 1676 1678\n",
      "1458 1237 1239 1257 1258 1259 1437 1438 1439 1440 1456 1457 1459 1478 1658\n",
      "1459 1259 1439 1440 1441 1457 1458 1460 1478 1479 1640 1658 1659 1660 1678\n",
      "1460 1241 1259 1260 1261 1279 1440 1441 1459 1461 1462 1478 1479 1480 1660\n",
      "1461 1261 1441 1460 1462 1463 1479 1480 1481 1482 1660 1661 1662 1680 1682\n",
      "1462 1241 1243 1261 1262 1263 1441 1442 1443 1460 1461 1463 1464 1482 1662\n",
      "1463 1263 1443 1461 1462 1464 1465 1482 1483 1484 1662 1663 1664 1682 1684\n",
      "1464 1243 1245 1263 1264 1265 1443 1444 1445 1462 1463 1465 1466 1484 1664\n",
      "1465 1265 1445 1463 1464 1466 1467 1484 1485 1486 1664 1665 1666 1684 1686\n",
      "1466 1245 1247 1265 1266 1267 1445 1446 1447 1464 1465 1467 1468 1486 1666\n",
      "1467 1267 1447 1465 1466 1468 1469 1486 1487 1488 1666 1667 1668 1686 1688\n",
      "1468 1247 1249 1267 1268 1269 1447 1448 1449 1466 1467 1469 1470 1488 1668\n",
      "1469 1269 1449 1467 1468 1470 1471 1488 1489 1490 1668 1669 1670 1688 1690\n",
      "1470 1249 1251 1269 1270 1271 1449 1450 1451 1468 1469 1471 1472 1490 1670\n",
      "1471 1271 1451 1469 1470 1472 1473 1490 1491 1492 1670 1671 1672 1690 1692\n",
      "1472 1251 1253 1271 1272 1273 1451 1452 1453 1470 1471 1473 1474 1492 1672\n",
      "1473 1273 1453 1471 1472 1474 1475 1492 1493 1494 1672 1673 1674 1692 1694\n",
      "1474 1253 1255 1273 1274 1275 1453 1454 1455 1472 1473 1475 1476 1494 1674\n",
      "1475 1275 1455 1473 1474 1476 1477 1494 1495 1496 1674 1675 1676 1694 1696\n",
      "1476 1255 1257 1275 1276 1277 1455 1456 1457 1474 1475 1477 1478 1496 1676\n",
      "1477 1277 1457 1475 1476 1478 1479 1496 1497 1498 1676 1677 1678 1696 1698\n",
      "1478 1257 1259 1277 1278 1279 1457 1458 1459 1460 1476 1477 1479 1498 1678\n",
      "1479 1279 1459 1460 1461 1477 1478 1480 1498 1499 1660 1678 1679 1680 1698\n",
      "1480 1261 1279 1280 1281 1299 1460 1461 1479 1481 1482 1498 1499 1500 1680\n",
      "1481 1281 1461 1480 1482 1483 1499 1500 1501 1502 1680 1681 1682 1700 1702\n",
      "1482 1261 1263 1281 1282 1283 1461 1462 1463 1480 1481 1483 1484 1502 1682\n",
      "1483 1283 1463 1481 1482 1484 1485 1502 1503 1504 1682 1683 1684 1702 1704\n",
      "1484 1263 1265 1283 1284 1285 1463 1464 1465 1482 1483 1485 1486 1504 1684\n",
      "1485 1285 1465 1483 1484 1486 1487 1504 1505 1506 1684 1685 1686 1704 1706\n",
      "1486 1265 1267 1285 1286 1287 1465 1466 1467 1484 1485 1487 1488 1506 1686\n",
      "1487 1287 1467 1485 1486 1488 1489 1506 1507 1508 1686 1687 1688 1706 1708\n",
      "1488 1267 1269 1287 1288 1289 1467 1468 1469 1486 1487 1489 1490 1508 1688\n",
      "1489 1289 1469 1487 1488 1490 1491 1508 1509 1510 1688 1689 1690 1708 1710\n",
      "1490 1269 1271 1289 1290 1291 1469 1470 1471 1488 1489 1491 1492 1510 1690\n",
      "1491 1291 1471 1489 1490 1492 1493 1510 1511 1512 1690 1691 1692 1710 1712\n",
      "1492 1271 1273 1291 1292 1293 1471 1472 1473 1490 1491 1493 1494 1512 1692\n",
      "1493 1293 1473 1491 1492 1494 1495 1512 1513 1514 1692 1693 1694 1712 1714\n",
      "1494 1273 1275 1293 1294 1295 1473 1474 1475 1492 1493 1495 1496 1514 1694\n",
      "1495 1295 1475 1493 1494 1496 1497 1514 1515 1516 1694 1695 1696 1714 1716\n",
      "1496 1275 1277 1295 1296 1297 1475 1476 1477 1494 1495 1497 1498 1516 1696\n",
      "1497 1297 1477 1495 1496 1498 1499 1516 1517 1518 1696 1697 1698 1716 1718\n",
      "1498 1277 1279 1297 1298 1299 1477 1478 1479 1480 1496 1497 1499 1518 1698\n",
      "1499 1299 1479 1480 1481 1497 1498 1500 1518 1519 1680 1698 1699 1700 1718\n",
      "1500 1281 1299 1300 1301 1319 1480 1481 1499 1501 1502 1518 1519 1520 1700\n",
      "1501 1301 1481 1500 1502 1503 1519 1520 1521 1522 1700 1701 1702 1720 1722\n",
      "1502 1281 1283 1301 1302 1303 1481 1482 1483 1500 1501 1503 1504 1522 1702\n",
      "1503 1303 1483 1501 1502 1504 1505 1522 1523 1524 1702 1703 1704 1722 1724\n",
      "1504 1283 1285 1303 1304 1305 1483 1484 1485 1502 1503 1505 1506 1524 1704\n",
      "1505 1305 1485 1503 1504 1506 1507 1524 1525 1526 1704 1705 1706 1724 1726\n",
      "1506 1285 1287 1305 1306 1307 1485 1486 1487 1504 1505 1507 1508 1526 1706\n",
      "1507 1307 1487 1505 1506 1508 1509 1526 1527 1528 1706 1707 1708 1726 1728\n",
      "1508 1287 1289 1307 1308 1309 1487 1488 1489 1506 1507 1509 1510 1528 1708\n",
      "1509 1309 1489 1507 1508 1510 1511 1528 1529 1530 1708 1709 1710 1728 1730\n",
      "1510 1289 1291 1309 1310 1311 1489 1490 1491 1508 1509 1511 1512 1530 1710\n",
      "1511 1311 1491 1509 1510 1512 1513 1530 1531 1532 1710 1711 1712 1730 1732\n",
      "1512 1291 1293 1311 1312 1313 1491 1492 1493 1510 1511 1513 1514 1532 1712\n",
      "1513 1313 1493 1511 1512 1514 1515 1532 1533 1534 1712 1713 1714 1732 1734\n",
      "1514 1293 1295 1313 1314 1315 1493 1494 1495 1512 1513 1515 1516 1534 1714\n",
      "1515 1315 1495 1513 1514 1516 1517 1534 1535 1536 1714 1715 1716 1734 1736\n",
      "1516 1295 1297 1315 1316 1317 1495 1496 1497 1514 1515 1517 1518 1536 1716\n",
      "1517 1317 1497 1515 1516 1518 1519 1536 1537 1538 1716 1717 1718 1736 1738\n",
      "1518 1297 1299 1317 1318 1319 1497 1498 1499 1500 1516 1517 1519 1538 1718\n",
      "1519 1319 1499 1500 1501 1517 1518 1520 1538 1539 1700 1718 1719 1720 1738\n",
      "1520 1301 1319 1320 1321 1339 1500 1501 1519 1521 1522 1538 1539 1540 1720\n",
      "1521 1321 1501 1520 1522 1523 1539 1540 1541 1542 1720 1721 1722 1740 1742\n",
      "1522 1301 1303 1321 1322 1323 1501 1502 1503 1520 1521 1523 1524 1542 1722\n",
      "1523 1323 1503 1521 1522 1524 1525 1542 1543 1544 1722 1723 1724 1742 1744\n",
      "1524 1303 1305 1323 1324 1325 1503 1504 1505 1522 1523 1525 1526 1544 1724\n",
      "1525 1325 1505 1523 1524 1526 1527 1544 1545 1546 1724 1725 1726 1744 1746\n",
      "1526 1305 1307 1325 1326 1327 1505 1506 1507 1524 1525 1527 1528 1546 1726\n",
      "1527 1327 1507 1525 1526 1528 1529 1546 1547 1548 1726 1727 1728 1746 1748\n",
      "1528 1307 1309 1327 1328 1329 1507 1508 1509 1526 1527 1529 1530 1548 1728\n",
      "1529 1329 1509 1527 1528 1530 1531 1548 1549 1550 1728 1729 1730 1748 1750\n",
      "1530 1309 1311 1329 1330 1331 1509 1510 1511 1528 1529 1531 1532 1550 1730\n",
      "1531 1331 1511 1529 1530 1532 1533 1550 1551 1552 1730 1731 1732 1750 1752\n",
      "1532 1311 1313 1331 1332 1333 1511 1512 1513 1530 1531 1533 1534 1552 1732\n",
      "1533 1333 1513 1531 1532 1534 1535 1552 1553 1554 1732 1733 1734 1752 1754\n",
      "1534 1313 1315 1333 1334 1335 1513 1514 1515 1532 1533 1535 1536 1554 1734\n",
      "1535 1335 1515 1533 1534 1536 1537 1554 1555 1556 1734 1735 1736 1754 1756\n",
      "1536 1315 1317 1335 1336 1337 1515 1516 1517 1534 1535 1537 1538 1556 1736\n",
      "1537 1337 1517 1535 1536 1538 1539 1556 1557 1558 1736 1737 1738 1756 1758\n",
      "1538 1317 1319 1337 1338 1339 1517 1518 1519 1520 1536 1537 1539 1558 1738\n",
      "1539 1339 1519 1520 1521 1537 1538 1540 1558 1559 1720 1738 1739 1740 1758\n",
      "1540 1321 1339 1340 1341 1359 1520 1521 1539 1541 1542 1558 1559 1560 1740\n",
      "1541 1341 1521 1540 1542 1543 1559 1560 1561 1562 1740 1741 1742 1760 1762\n",
      "1542 1321 1323 1341 1342 1343 1521 1522 1523 1540 1541 1543 1544 1562 1742\n",
      "1543 1343 1523 1541 1542 1544 1545 1562 1563 1564 1742 1743 1744 1762 1764\n",
      "1544 1323 1325 1343 1344 1345 1523 1524 1525 1542 1543 1545 1546 1564 1744\n",
      "1545 1345 1525 1543 1544 1546 1547 1564 1565 1566 1744 1745 1746 1764 1766\n",
      "1546 1325 1327 1345 1346 1347 1525 1526 1527 1544 1545 1547 1548 1566 1746\n",
      "1547 1347 1527 1545 1546 1548 1549 1566 1567 1568 1746 1747 1748 1766 1768\n",
      "1548 1327 1329 1347 1348 1349 1527 1528 1529 1546 1547 1549 1550 1568 1748\n",
      "1549 1349 1529 1547 1548 1550 1551 1568 1569 1570 1748 1749 1750 1768 1770\n",
      "1550 1329 1331 1349 1350 1351 1529 1530 1531 1548 1549 1551 1552 1570 1750\n",
      "1551 1351 1531 1549 1550 1552 1553 1570 1571 1572 1750 1751 1752 1770 1772\n",
      "1552 1331 1333 1351 1352 1353 1531 1532 1533 1550 1551 1553 1554 1572 1752\n",
      "1553 1353 1533 1551 1552 1554 1555 1572 1573 1574 1752 1753 1754 1772 1774\n",
      "1554 1333 1335 1353 1354 1355 1533 1534 1535 1552 1553 1555 1556 1574 1754\n",
      "1555 1355 1535 1553 1554 1556 1557 1574 1575 1576 1754 1755 1756 1774 1776\n",
      "1556 1335 1337 1355 1356 1357 1535 1536 1537 1554 1555 1557 1558 1576 1756\n",
      "1557 1357 1537 1555 1556 1558 1559 1576 1577 1578 1756 1757 1758 1776 1778\n",
      "1558 1337 1339 1357 1358 1359 1537 1538 1539 1540 1556 1557 1559 1578 1758\n",
      "1559 1359 1539 1540 1541 1557 1558 1560 1578 1579 1740 1758 1759 1760 1778\n",
      "1560 1341 1359 1360 1361 1379 1540 1541 1559 1561 1562 1578 1579 1580 1760\n",
      "1561 1361 1541 1560 1562 1563 1579 1580 1581 1582 1760 1761 1762 1780 1782\n",
      "1562 1341 1343 1361 1362 1363 1541 1542 1543 1560 1561 1563 1564 1582 1762\n",
      "1563 1363 1543 1561 1562 1564 1565 1582 1583 1584 1762 1763 1764 1782 1784\n",
      "1564 1343 1345 1363 1364 1365 1543 1544 1545 1562 1563 1565 1566 1584 1764\n",
      "1565 1365 1545 1563 1564 1566 1567 1584 1585 1586 1764 1765 1766 1784 1786\n",
      "1566 1345 1347 1365 1366 1367 1545 1546 1547 1564 1565 1567 1568 1586 1766\n",
      "1567 1367 1547 1565 1566 1568 1569 1586 1587 1588 1766 1767 1768 1786 1788\n",
      "1568 1347 1349 1367 1368 1369 1547 1548 1549 1566 1567 1569 1570 1588 1768\n",
      "1569 1369 1549 1567 1568 1570 1571 1588 1589 1590 1768 1769 1770 1788 1790\n",
      "1570 1349 1351 1369 1370 1371 1549 1550 1551 1568 1569 1571 1572 1590 1770\n",
      "1571 1371 1551 1569 1570 1572 1573 1590 1591 1592 1770 1771 1772 1790 1792\n",
      "1572 1351 1353 1371 1372 1373 1551 1552 1553 1570 1571 1573 1574 1592 1772\n",
      "1573 1373 1553 1571 1572 1574 1575 1592 1593 1594 1772 1773 1774 1792 1794\n",
      "1574 1353 1355 1373 1374 1375 1553 1554 1555 1572 1573 1575 1576 1594 1774\n",
      "1575 1375 1555 1573 1574 1576 1577 1594 1595 1596 1774 1775 1776 1794 1796\n",
      "1576 1355 1357 1375 1376 1377 1555 1556 1557 1574 1575 1577 1578 1596 1776\n",
      "1577 1377 1557 1575 1576 1578 1579 1596 1597 1598 1776 1777 1778 1796 1798\n",
      "1578 1357 1359 1377 1378 1379 1557 1558 1559 1560 1576 1577 1579 1598 1778\n",
      "1579 1379 1559 1560 1561 1577 1578 1580 1598 1599 1760 1778 1779 1780 1798\n",
      "1580 1361 1379 1380 1381 1399 1400 1560 1561 1579 1581 1582 1598 1599 1780\n",
      "1581 1381 1400 1401 1402 1561 1580 1582 1583 1599 1600 1602 1780 1781 1782\n",
      "1582 1361 1363 1381 1382 1383 1402 1561 1562 1563 1580 1581 1583 1584 1782\n",
      "1583 1383 1402 1403 1404 1563 1581 1582 1584 1585 1602 1604 1782 1783 1784\n",
      "1584 1363 1365 1383 1384 1385 1404 1563 1564 1565 1582 1583 1585 1586 1784\n",
      "1585 1385 1404 1405 1406 1565 1583 1584 1586 1587 1604 1606 1784 1785 1786\n",
      "1586 1365 1367 1385 1386 1387 1406 1565 1566 1567 1584 1585 1587 1588 1786\n",
      "1587 1387 1406 1407 1408 1567 1585 1586 1588 1589 1606 1608 1786 1787 1788\n",
      "1588 1367 1369 1387 1388 1389 1408 1567 1568 1569 1586 1587 1589 1590 1788\n",
      "1589 1389 1408 1409 1410 1569 1587 1588 1590 1591 1608 1610 1788 1789 1790\n",
      "1590 1369 1371 1389 1390 1391 1410 1569 1570 1571 1588 1589 1591 1592 1790\n",
      "1591 1391 1410 1411 1412 1571 1589 1590 1592 1593 1610 1612 1790 1791 1792\n",
      "1592 1371 1373 1391 1392 1393 1412 1571 1572 1573 1590 1591 1593 1594 1792\n",
      "1593 1393 1412 1413 1414 1573 1591 1592 1594 1595 1612 1614 1792 1793 1794\n",
      "1594 1373 1375 1393 1394 1395 1414 1573 1574 1575 1592 1593 1595 1596 1794\n",
      "1595 1395 1414 1415 1416 1575 1593 1594 1596 1597 1614 1616 1794 1795 1796\n",
      "1596 1375 1377 1395 1396 1397 1416 1575 1576 1577 1594 1595 1597 1598 1796\n",
      "1597 1397 1416 1417 1418 1577 1595 1596 1598 1599 1616 1618 1796 1797 1798\n",
      "1598 1377 1379 1397 1398 1399 1418 1577 1578 1579 1580 1596 1597 1599 1798\n",
      "1599 1399 1400 1418 1419 1579 1580 1581 1597 1598 1600 1618 1780 1798 1799\n",
      "1600 1400 1401 1419 1581 1599 1601 1602 1618 1619 1620 1780 1781 1799 1800\n",
      "1601 1401 1600 1602 1603 1619 1620 1621 1622 1781 1800 1801 1802 1820 1822\n",
      "1602 1401 1402 1403 1581 1583 1600 1601 1603 1604 1622 1781 1782 1783 1802\n",
      "1603 1403 1601 1602 1604 1605 1622 1623 1624 1783 1802 1803 1804 1822 1824\n",
      "1604 1403 1404 1405 1583 1585 1602 1603 1605 1606 1624 1783 1784 1785 1804\n",
      "1605 1405 1603 1604 1606 1607 1624 1625 1626 1785 1804 1805 1806 1824 1826\n",
      "1606 1405 1406 1407 1585 1587 1604 1605 1607 1608 1626 1785 1786 1787 1806\n",
      "1607 1407 1605 1606 1608 1609 1626 1627 1628 1787 1806 1807 1808 1826 1828\n",
      "1608 1407 1408 1409 1587 1589 1606 1607 1609 1610 1628 1787 1788 1789 1808\n",
      "1609 1409 1607 1608 1610 1611 1628 1629 1630 1789 1808 1809 1810 1828 1830\n",
      "1610 1409 1410 1411 1589 1591 1608 1609 1611 1612 1630 1789 1790 1791 1810\n",
      "1611 1411 1609 1610 1612 1613 1630 1631 1632 1791 1810 1811 1812 1830 1832\n",
      "1612 1411 1412 1413 1591 1593 1610 1611 1613 1614 1632 1791 1792 1793 1812\n",
      "1613 1413 1611 1612 1614 1615 1632 1633 1634 1793 1812 1813 1814 1832 1834\n",
      "1614 1413 1414 1415 1593 1595 1612 1613 1615 1616 1634 1793 1794 1795 1814\n",
      "1615 1415 1613 1614 1616 1617 1634 1635 1636 1795 1814 1815 1816 1834 1836\n",
      "1616 1415 1416 1417 1595 1597 1614 1615 1617 1618 1636 1795 1796 1797 1816\n",
      "1617 1417 1615 1616 1618 1619 1636 1637 1638 1797 1816 1817 1818 1836 1838\n",
      "1618 1417 1418 1419 1597 1599 1600 1616 1617 1619 1638 1797 1798 1799 1818\n",
      "1619 1419 1600 1601 1617 1618 1620 1638 1639 1799 1800 1818 1819 1820 1838\n",
      "1620 1401 1419 1420 1421 1439 1600 1601 1619 1621 1622 1638 1639 1640 1820\n",
      "1621 1421 1601 1620 1622 1623 1639 1640 1641 1642 1820 1821 1822 1840 1842\n",
      "1622 1401 1403 1421 1422 1423 1601 1602 1603 1620 1621 1623 1624 1642 1822\n",
      "1623 1423 1603 1621 1622 1624 1625 1642 1643 1644 1822 1823 1824 1842 1844\n",
      "1624 1403 1405 1423 1424 1425 1603 1604 1605 1622 1623 1625 1626 1644 1824\n",
      "1625 1425 1605 1623 1624 1626 1627 1644 1645 1646 1824 1825 1826 1844 1846\n",
      "1626 1405 1407 1425 1426 1427 1605 1606 1607 1624 1625 1627 1628 1646 1826\n",
      "1627 1427 1607 1625 1626 1628 1629 1646 1647 1648 1826 1827 1828 1846 1848\n",
      "1628 1407 1409 1427 1428 1429 1607 1608 1609 1626 1627 1629 1630 1648 1828\n",
      "1629 1429 1609 1627 1628 1630 1631 1648 1649 1650 1828 1829 1830 1848 1850\n",
      "1630 1409 1411 1429 1430 1431 1609 1610 1611 1628 1629 1631 1632 1650 1830\n",
      "1631 1431 1611 1629 1630 1632 1633 1650 1651 1652 1830 1831 1832 1850 1852\n",
      "1632 1411 1413 1431 1432 1433 1611 1612 1613 1630 1631 1633 1634 1652 1832\n",
      "1633 1433 1613 1631 1632 1634 1635 1652 1653 1654 1832 1833 1834 1852 1854\n",
      "1634 1413 1415 1433 1434 1435 1613 1614 1615 1632 1633 1635 1636 1654 1834\n",
      "1635 1435 1615 1633 1634 1636 1637 1654 1655 1656 1834 1835 1836 1854 1856\n",
      "1636 1415 1417 1435 1436 1437 1615 1616 1617 1634 1635 1637 1638 1656 1836\n",
      "1637 1437 1617 1635 1636 1638 1639 1656 1657 1658 1836 1837 1838 1856 1858\n",
      "1638 1417 1419 1437 1438 1439 1617 1618 1619 1620 1636 1637 1639 1658 1838\n",
      "1639 1439 1619 1620 1621 1637 1638 1640 1658 1659 1820 1838 1839 1840 1858\n",
      "1640 1421 1439 1440 1441 1459 1620 1621 1639 1641 1642 1658 1659 1660 1840\n",
      "1641 1441 1621 1640 1642 1643 1659 1660 1661 1662 1840 1841 1842 1860 1862\n",
      "1642 1421 1423 1441 1442 1443 1621 1622 1623 1640 1641 1643 1644 1662 1842\n",
      "1643 1443 1623 1641 1642 1644 1645 1662 1663 1664 1842 1843 1844 1862 1864\n",
      "1644 1423 1425 1443 1444 1445 1623 1624 1625 1642 1643 1645 1646 1664 1844\n",
      "1645 1445 1625 1643 1644 1646 1647 1664 1665 1666 1844 1845 1846 1864 1866\n",
      "1646 1425 1427 1445 1446 1447 1625 1626 1627 1644 1645 1647 1648 1666 1846\n",
      "1647 1447 1627 1645 1646 1648 1649 1666 1667 1668 1846 1847 1848 1866 1868\n",
      "1648 1427 1429 1447 1448 1449 1627 1628 1629 1646 1647 1649 1650 1668 1848\n",
      "1649 1449 1629 1647 1648 1650 1651 1668 1669 1670 1848 1849 1850 1868 1870\n",
      "1650 1429 1431 1449 1450 1451 1629 1630 1631 1648 1649 1651 1652 1670 1850\n",
      "1651 1451 1631 1649 1650 1652 1653 1670 1671 1672 1850 1851 1852 1870 1872\n",
      "1652 1431 1433 1451 1452 1453 1631 1632 1633 1650 1651 1653 1654 1672 1852\n",
      "1653 1453 1633 1651 1652 1654 1655 1672 1673 1674 1852 1853 1854 1872 1874\n",
      "1654 1433 1435 1453 1454 1455 1633 1634 1635 1652 1653 1655 1656 1674 1854\n",
      "1655 1455 1635 1653 1654 1656 1657 1674 1675 1676 1854 1855 1856 1874 1876\n",
      "1656 1435 1437 1455 1456 1457 1635 1636 1637 1654 1655 1657 1658 1676 1856\n",
      "1657 1457 1637 1655 1656 1658 1659 1676 1677 1678 1856 1857 1858 1876 1878\n",
      "1658 1437 1439 1457 1458 1459 1637 1638 1639 1640 1656 1657 1659 1678 1858\n",
      "1659 1459 1639 1640 1641 1657 1658 1660 1678 1679 1840 1858 1859 1860 1878\n",
      "1660 1441 1459 1460 1461 1479 1640 1641 1659 1661 1662 1678 1679 1680 1860\n",
      "1661 1461 1641 1660 1662 1663 1679 1680 1681 1682 1860 1861 1862 1880 1882\n",
      "1662 1441 1443 1461 1462 1463 1641 1642 1643 1660 1661 1663 1664 1682 1862\n",
      "1663 1463 1643 1661 1662 1664 1665 1682 1683 1684 1862 1863 1864 1882 1884\n",
      "1664 1443 1445 1463 1464 1465 1643 1644 1645 1662 1663 1665 1666 1684 1864\n",
      "1665 1465 1645 1663 1664 1666 1667 1684 1685 1686 1864 1865 1866 1884 1886\n",
      "1666 1445 1447 1465 1466 1467 1645 1646 1647 1664 1665 1667 1668 1686 1866\n",
      "1667 1467 1647 1665 1666 1668 1669 1686 1687 1688 1866 1867 1868 1886 1888\n",
      "1668 1447 1449 1467 1468 1469 1647 1648 1649 1666 1667 1669 1670 1688 1868\n",
      "1669 1469 1649 1667 1668 1670 1671 1688 1689 1690 1868 1869 1870 1888 1890\n",
      "1670 1449 1451 1469 1470 1471 1649 1650 1651 1668 1669 1671 1672 1690 1870\n",
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      "1922 122 1701 1703 1721 1722 1723 1901 1902 1903 1920 1921 1923 1924 1942\n",
      "1923 122 123 124 142 144 1723 1903 1921 1922 1924 1925 1942 1943 1944\n",
      "1924 124 1703 1705 1723 1724 1725 1903 1904 1905 1922 1923 1925 1926 1944\n",
      "1925 124 125 126 144 146 1725 1905 1923 1924 1926 1927 1944 1945 1946\n",
      "1926 126 1705 1707 1725 1726 1727 1905 1906 1907 1924 1925 1927 1928 1946\n",
      "1927 126 127 128 146 148 1727 1907 1925 1926 1928 1929 1946 1947 1948\n",
      "1928 128 1707 1709 1727 1728 1729 1907 1908 1909 1926 1927 1929 1930 1948\n",
      "1929 128 129 130 148 150 1729 1909 1927 1928 1930 1931 1948 1949 1950\n",
      "1930 130 1709 1711 1729 1730 1731 1909 1910 1911 1928 1929 1931 1932 1950\n",
      "1931 130 131 132 150 152 1731 1911 1929 1930 1932 1933 1950 1951 1952\n",
      "1932 132 1711 1713 1731 1732 1733 1911 1912 1913 1930 1931 1933 1934 1952\n",
      "1933 132 133 134 152 154 1733 1913 1931 1932 1934 1935 1952 1953 1954\n",
      "1934 134 1713 1715 1733 1734 1735 1913 1914 1915 1932 1933 1935 1936 1954\n",
      "1935 134 135 136 154 156 1735 1915 1933 1934 1936 1937 1954 1955 1956\n",
      "1936 136 1715 1717 1735 1736 1737 1915 1916 1917 1934 1935 1937 1938 1956\n",
      "1937 136 137 138 156 158 1737 1917 1935 1936 1938 1939 1956 1957 1958\n",
      "1938 138 1717 1719 1737 1738 1739 1917 1918 1919 1920 1936 1937 1939 1958\n",
      "1939 120 138 139 140 158 1739 1919 1920 1921 1937 1938 1940 1958 1959\n",
      "1940 140 1721 1739 1740 1741 1759 1920 1921 1939 1941 1942 1958 1959 1960\n",
      "1941 140 141 142 160 162 1741 1921 1940 1942 1943 1959 1960 1961 1962\n",
      "1942 142 1721 1723 1741 1742 1743 1921 1922 1923 1940 1941 1943 1944 1962\n",
      "1943 142 143 144 162 164 1743 1923 1941 1942 1944 1945 1962 1963 1964\n",
      "1944 144 1723 1725 1743 1744 1745 1923 1924 1925 1942 1943 1945 1946 1964\n",
      "1945 144 145 146 164 166 1745 1925 1943 1944 1946 1947 1964 1965 1966\n",
      "1946 146 1725 1727 1745 1746 1747 1925 1926 1927 1944 1945 1947 1948 1966\n",
      "1947 146 147 148 166 168 1747 1927 1945 1946 1948 1949 1966 1967 1968\n",
      "1948 148 1727 1729 1747 1748 1749 1927 1928 1929 1946 1947 1949 1950 1968\n",
      "1949 148 149 150 168 170 1749 1929 1947 1948 1950 1951 1968 1969 1970\n",
      "1950 150 1729 1731 1749 1750 1751 1929 1930 1931 1948 1949 1951 1952 1970\n",
      "1951 150 151 152 170 172 1751 1931 1949 1950 1952 1953 1970 1971 1972\n",
      "1952 152 1731 1733 1751 1752 1753 1931 1932 1933 1950 1951 1953 1954 1972\n",
      "1953 152 153 154 172 174 1753 1933 1951 1952 1954 1955 1972 1973 1974\n",
      "1954 154 1733 1735 1753 1754 1755 1933 1934 1935 1952 1953 1955 1956 1974\n",
      "1955 154 155 156 174 176 1755 1935 1953 1954 1956 1957 1974 1975 1976\n",
      "1956 156 1735 1737 1755 1756 1757 1935 1936 1937 1954 1955 1957 1958 1976\n",
      "1957 156 157 158 176 178 1757 1937 1955 1956 1958 1959 1976 1977 1978\n",
      "1958 158 1737 1739 1757 1758 1759 1937 1938 1939 1940 1956 1957 1959 1978\n",
      "1959 140 158 159 160 178 1759 1939 1940 1941 1957 1958 1960 1978 1979\n",
      "1960 160 1741 1759 1760 1761 1779 1940 1941 1959 1961 1962 1978 1979 1980\n",
      "1961 160 161 162 180 182 1761 1941 1960 1962 1963 1979 1980 1981 1982\n",
      "1962 162 1741 1743 1761 1762 1763 1941 1942 1943 1960 1961 1963 1964 1982\n",
      "1963 162 163 164 182 184 1763 1943 1961 1962 1964 1965 1982 1983 1984\n",
      "1964 164 1743 1745 1763 1764 1765 1943 1944 1945 1962 1963 1965 1966 1984\n",
      "1965 164 165 166 184 186 1765 1945 1963 1964 1966 1967 1984 1985 1986\n",
      "1966 166 1745 1747 1765 1766 1767 1945 1946 1947 1964 1965 1967 1968 1986\n",
      "1967 166 167 168 186 188 1767 1947 1965 1966 1968 1969 1986 1987 1988\n",
      "1968 168 1747 1749 1767 1768 1769 1947 1948 1949 1966 1967 1969 1970 1988\n",
      "1969 168 169 170 188 190 1769 1949 1967 1968 1970 1971 1988 1989 1990\n",
      "1970 170 1749 1751 1769 1770 1771 1949 1950 1951 1968 1969 1971 1972 1990\n",
      "1971 170 171 172 190 192 1771 1951 1969 1970 1972 1973 1990 1991 1992\n",
      "1972 172 1751 1753 1771 1772 1773 1951 1952 1953 1970 1971 1973 1974 1992\n",
      "1973 172 173 174 192 194 1773 1953 1971 1972 1974 1975 1992 1993 1994\n",
      "1974 174 1753 1755 1773 1774 1775 1953 1954 1955 1972 1973 1975 1976 1994\n",
      "1975 174 175 176 194 196 1775 1955 1973 1974 1976 1977 1994 1995 1996\n",
      "1976 176 1755 1757 1775 1776 1777 1955 1956 1957 1974 1975 1977 1978 1996\n",
      "1977 176 177 178 196 198 1777 1957 1975 1976 1978 1979 1996 1997 1998\n",
      "1978 178 1757 1759 1777 1778 1779 1957 1958 1959 1960 1976 1977 1979 1998\n",
      "1979 160 178 179 180 198 1779 1959 1960 1961 1977 1978 1980 1998 1999\n",
      "1980 180 1761 1779 1780 1781 1799 1800 1960 1961 1979 1981 1982 1998 1999\n",
      "1981 0 2 180 181 182 1781 1800 1801 1802 1961 1980 1982 1983 1999\n",
      "1982 182 1761 1763 1781 1782 1783 1802 1961 1962 1963 1980 1981 1983 1984\n",
      "1983 2 4 182 183 184 1783 1802 1803 1804 1963 1981 1982 1984 1985\n",
      "1984 184 1763 1765 1783 1784 1785 1804 1963 1964 1965 1982 1983 1985 1986\n",
      "1985 4 6 184 185 186 1785 1804 1805 1806 1965 1983 1984 1986 1987\n",
      "1986 186 1765 1767 1785 1786 1787 1806 1965 1966 1967 1984 1985 1987 1988\n",
      "1987 6 8 186 187 188 1787 1806 1807 1808 1967 1985 1986 1988 1989\n",
      "1988 188 1767 1769 1787 1788 1789 1808 1967 1968 1969 1986 1987 1989 1990\n",
      "1989 8 10 188 189 190 1789 1808 1809 1810 1969 1987 1988 1990 1991\n",
      "1990 190 1769 1771 1789 1790 1791 1810 1969 1970 1971 1988 1989 1991 1992\n",
      "1991 10 12 190 191 192 1791 1810 1811 1812 1971 1989 1990 1992 1993\n",
      "1992 192 1771 1773 1791 1792 1793 1812 1971 1972 1973 1990 1991 1993 1994\n",
      "1993 12 14 192 193 194 1793 1812 1813 1814 1973 1991 1992 1994 1995\n",
      "1994 194 1773 1775 1793 1794 1795 1814 1973 1974 1975 1992 1993 1995 1996\n",
      "1995 14 16 194 195 196 1795 1814 1815 1816 1975 1993 1994 1996 1997\n",
      "1996 196 1775 1777 1795 1796 1797 1816 1975 1976 1977 1994 1995 1997 1998\n",
      "1997 16 18 196 197 198 1797 1816 1817 1818 1977 1995 1996 1998 1999\n",
      "1998 198 1777 1779 1797 1798 1799 1818 1977 1978 1979 1980 1996 1997 1999\n",
      "1999 0 18 180 198 199 1799 1800 1818 1819 1979 1980 1981 1997 1998\n",
      "\n"
     ]
    }
   ],
   "source": [
    "neighbors.dump('neighborlist.txt')\n",
    "\n",
    "with open('neighborlist.txt') as f:\n",
    "    print(f.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2. load()\n",
    "\n",
    "Loads the dumped content into an existing NeighborList object.\n",
    "\n",
    "Parameters\n",
    " \n",
    "- **model** (*str or file-like object*) Gives the file path or content to load."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average number of neighbors = 14.0\n"
     ]
    }
   ],
   "source": [
    "neighbors.load('neighborlist.txt')\n",
    "print('Average number of neighbors =', neighbors.coord.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3. Load on initializing\n",
    "\n",
    "The content can also be loaded during initialization using the model parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average number of neighbors = 14.0\n"
     ]
    }
   ],
   "source": [
    "neighbors = am.NeighborList(model='neighborlist.txt')\n",
    "print('Average number of neighbors =', neighbors.coord.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**File Cleanup**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.remove('neighborlist.txt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  "
   ]
  }
 ],
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    "name": "ipython",
    "version": 3
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